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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 15:59
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Checking Account:
  • Deposit €14,000 (gets €500 bonus, as €14,000 ≥ €14,000)
[*]Savings Account:

  • Deposit the remaining €6,000 (earns 3% interest since < €8,000)
Inequalities:
  • Checking: €14,000 ≥ deposit ≥ €14,000 → bonus = €500.
  • Savings: €6,000 ≥ deposit < €8,000 → interest = 3%.
Total Balance:
  • Checking: €14,000 + €500 = €14,500.
  • Savings: €6,000 × 1.03 = €6,180.
Total = €20,680.

Selections:
  • Checking Account: €14,000
  • Savings Account: €6,000

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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 16:50
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If she deposits 14000 in the checking account and 6000 in the savings account, she gets 500 and 180 (3% of 6000). Total 680
If she deposits 10000 in the checking account and 10000 in the savings account, she gets 300 and 400 (4% of 10000). Total 700
If she deposits 6000 in the checking account and 14000 in the savings account, she gets 100 and 560 (4% of 14000). Total 660

Answer: The best option for her is to deposit 10000 in the checking account and 10000 in the savings account.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 17:33
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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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Case 1: 6000(checking) + 14000(saving) => 100 + 560 => 660
Case 2: 8000(checking) + 12000(saving) => 100 + 480 => 580
Case 3: 10000(checking) + 10000(saving) => 300 + 400 => 700
Case 4: 12000(checking) + 8000(saving) => 300 + 320 => 620
Case 5: 14000(checking) + 6000(saving) => 500 + 180=> 680
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to Updated on: 18 Dec 2024, 18:58
Originally posted by MURALIKA on 17 Dec 2024, 20:25.
Last edited by MURALIKA on 18 Dec 2024, 18:58, edited 1 time in total.
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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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To maximize the year end balance,
She must deposit 10000 in her CHecking accunt and 10000 in her savings account
10000+300+10000*4% = 20700
If we check each and every option, the maximum amount comes when C = 10000 and S = 10000
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 20:45
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Checking AccountSavings AccountChecking A/c value addedSavings A/c interestTotal value added
600014000100560660
800012000100480580
1000010000300400700
120008000300320620
140006000500180680

The above shows possible combinations, hence the 3rd gives the best possible value add
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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 22:43
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Let's look at various cases:

Total deposit constraint:
\(\text{Checking deposit} + \text{Savings deposit} = €20,000\)

Case 1:
\(\text{Checking} = €6,000, \text{Savings} = €14,000\)
\(\text{Checking balance} = €6,000 + €100 = €6,100\)
\(\text{Savings interest} = €14,000 \times 4% = €560\)
\(\text{Year-end balance} = €6,100 + €14,560 = €20,660\)

Case 2:
\(\text{Checking} = €8,000, \text{Savings} = €12,000\)
\(\text{Checking balance} = €8,000 + €100 = €8,100\)
\(\text{Savings interest} = €12,000 \times 4% = €480\)
\(\text{Year-end balance} = €8,100 + €12,480 = €20,580\)

Case 3:
\(\text{Checking} = €10,000, \text{Savings} = €10,000\)
\(\text{Checking balance} = €10,000 + €300 = €10,300\)
\(\text{Savings interest} = €10,000 \times 4% = €400\)
\(\text{Year-end balance} = €10,300 + €10,400 = €20,700\)

Case 4:
\(\text{Checking} = €12,000, \text{Savings} = €8,000\)
\(\text{Checking balance} = €12,000 + €300 = €12,300\)
\(\text{Savings interest} = €8,000 \times 4% = €320\)
\(\text{Year-end balance} = €12,300 + €8,320 = €20,620\)

Case 5:
\(\text{Checking} = €14,000, \text{Savings} = €6,000\)
\(\text{Checking balance} = €14,000 + €500 = €14,500\)
\(\text{Savings interest} = €6,000 \times 3% = €180\)
\(\text{Year-end balance} = €14,500 + €6,180 = €20,680\)

Final Answer:
  • \(\text{Checking Account} = €10,000\)
  • \(\text{Savings Account} = €10,000\)
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 23:54
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Case 1: €6,000 in Checking, €14,000 in Savings
Checking Account: €6,000 + €100 = €6,100.
Savings Account: €14,000 × 1.04 = €14,560.
Total Balance = €6,100 + €14,560 = €20,660.
Case 2: €8,000 in Checking, €12,000 in Savings
Checking Account: €8,000 + €100 = €8,100.
Savings Account: €12,000 × 1.04 = €12,480.
Total Balance = €8,100 + €12,480 = €20,580.
Case 3: €10,000 in Checking, €10,000 in Savings
Checking Account: €10,000 + €300 = €10,300.
Savings Account: €10,000 × 1.04 = €10,400.
Total Balance = €10,300 + €10,400 = €20,700.
Case 4: €12,000 in Checking, €8,000 in Savings
Checking Account: €12,000 + €300 = €12,300.
Savings Account: €8,000 × 1.04 = €8,320.
Total Balance = €12,300 + €8,320 = €20,620.
Case 5: €14,000 in Checking, €6,000 in Savings
Checking Account: €14,000 + €500 = €14,500.
Savings Account: €6,000 × 1.03 = €6,180.
Total Balance = €14,500 + €6,180 = €20,680.
Step 4: Determine the Optimal Distribution
The highest total year-end balance is €20,700, achieved by depositing €10,000 into the checking account and €10,000 into the savings account.

Final Answer:
Checking Account: €10,000
Savings Account: €10,000
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 17 Dec 2024, 23:56
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Let's look at all possible splits of 20k, and let's calculate the respective profit as per the conditions above, where the first sum is paid into the checking account and the second - into savings one.

(1) 6,000 and 14,000
After 1 year: \(6000 + 100\); and 14,000 + 4% = \( 14000 +560\)
Total gain: 660

(2) 8,000 and 12,000
After 1 year: \(8000 + 100\); and 12,000 + 4% = \( 12000 +480\)
Total gain: 580

(3) 10,000 and 10,000
After 1 year: \(10000 + 300\); and 10,000 + 4% = \( 10000 +400\)
Total gain: 700

(4) 12,000 and 8,000
After 1 year: \(12000 + 300\); and 8,000 + 4% = \( 8000+320\)
Total gain: 620

(5) 14,000 and 6000
After 1 year: \(14000 + 500\); and 6,000 + 3% = \( 14000 +180\)
Total gain: 680

Therefore, we see that the maximum profit is received in scenario 3, when the money is spread equally. The answer is 10k into each account.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 00:26
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Keeping in mind total sum is 20k, I sampled 3 values of the saving amount: 6k, 10k, and 14k
a. 6k saving, 14k checking
Checking: +500
Saving: +180 (3%)
Total: 680
b. 10k saving, 10k checking
Checking: +300
Saving: +400 (4%)
Total: 700
c. 14k saving, 6k checking
Checking: +100
Saving: +560
Total: 660

It looks to me that on either side of 10k, the total gain drops. Choose 10,000 for both saving and checking
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 01:05
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According to the information given in the question, Hana would deposit 20000 euros. The largest amount we would receive in checking account is 500 euros when we deposit at least 14000, and 3% in savings account if we deposit 6000 euros, hence we would receive a total of 680 euros.
Option 2 ) 12000 in checking account = 300 euro incentive and interest would 4% on 8000 euros = 320.
Total 620 euros
Option 3 ) 10,000 in checking account = 300 euro incentive and interest of 400 euros on 10,000 euros totalling 700 euros (Maximum)
Option 4 ) 8,000 in checking account = 100 euro incentive and interest of 480 euros on 12,000 euros totalling 580 euros
Option 5 ) 6,000 in checking account = 100 euro incentive and interest of 560 euros on 14,000 euros totalling 660 euros

Hence correct answer is 10,000 and 10,000.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 01:25
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Ans: Amount deposited in both checking account and savings account = €10,000

For checking account:
If 6,000<=Deposited Amount<10,000 then Credit union deposits = € 100
If 10,000<=Deposited Amount<14,000 then Credit union deposits = € 300
If Deposited Amount>=14,000 then Credit union deposits = € 500

For Savings Account:
If Deposited amount >= 8000 then interest = 4% otherwise the interest is 3%


As the amount that the credit union is giving is constant for certain intervals in case of checking account, Hana can maximize the interest by keeping the amount in the checking account minimal of the interval i.e., 6,000 or 10,000 or 14,000

Let Amount in Checking account be 14000 and in savings account be 6000
Extra money received from credit union and interest = 500 and ((6000*3*1)/100) = 500 and 180
So, total = 680

Let Amount in Checking account be 10000 and in savings account be 10000
Extra money received from credit union and interest = 300 and ((10000*4*1)/100) = 300 and 400
So, total = 700 (Maximum)

Let Amount in Checking account be 6000 and in savings account be 14000
Extra money received from credit union and interest = 100 and ((14000*4*1)/100) = 300 and 560
So, total = 6600

From this we can see, Hana receives the maximum amount when the amount in both checking account and savings account is 10,000
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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 01:33
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Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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Here i think going with option elimination will work effectively.

lets assume hana invested x amount in checking account and y in savings account.

x + y = 20000

Now if we see options we have pairs of (6k, 14k) (8k, 12k) and (10k, 10k)

lets take first pair and get the additional values to maximize year end balance.

I - i) first assuming x = 6000 and y = 14000
on 6000 investment in checking account we will get additional 100.
14000 investment in savings we will get 4% = 14000 * 4% = 560
Total additional = 560 + 100 = 660

ii) Now assuming x = 14000 and y= 6000
on 14000 in checking account we will get additional 500
on 6000 investment in saving we will get 3% = 6000 * 3% = 180
Total additional = 500 + 180 = 680

II - i) x=8000 and y=12000
on 8000 in checking we get 100
on 12000 in savings we will get 4% = 12000 * 4% = 480
Total additional = 100 + 480 = 580

ii) x=12000 and y=8000
on 12000 in checking we will get 300
on 8000 in savings we will get 4% = 8000 * 4% = 320
Total additional = 300 + 320 = 620

III - Now equal distribution x=10000 and y=10000
on 10000 checking we will get 300
and on 10000 saving we will get 4% = 10000 * 4% = 400
Total additional = 300 + 400 = 700
Therefore answer is 10000 for both.
Checking Account = 10000 and Saving Account = 10000.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 01:58
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Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

 


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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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Given Check deposit + Saving deposit €20,000, based on the choice available, we have the following potential combination
(1) Check deposit €6,000 + Saving deposit €14,000
(2) Check deposit €8,000 + Saving deposit €12,000
(3) Check deposit €10,000 + Saving deposit €10,000
(4) Check deposit €12,000 + Saving deposit €8,000
(5) Check deposit €14,000 + Saving deposit €6,000

Let's calculate each option separately:
(1) Check deposit addition €100 + Saving deposit interest €14,000*4% (€560) = €660
(2) Check deposit addition €100 + Saving deposit interest €12,000*4% (€480) = €580
(3) Check deposit addition €300 + Saving deposit interest €10,000*4% (€400) = €700 (✔)
(4) Check deposit addition €300 + Saving deposit interest €8,000*4% (€320) = €620
(5) Check deposit addition €500 + Saving deposit interest €6,000*3% (€180) = €680

Therefore the answer is C
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 02:01
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Hi Everyone :)

Checking account ("C"):
* No interest
6,000 <= C < 10,000 => +100
10,000 <= C < 14,000 => +300
14,000 <= C => +500

Saving account ("S"):
*Only interest
8,000 <= S => 4%
S < 8,000 => 3%

Total of 20,000$ distributed

options in general (by the answers):
CSEarnCEarnSTotal
600014000100560660
800012000100480580
1000010000300400700
120008000300320620
140006000500180680

10,000+10,000 - is our Answer :)
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 02:01
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Hi All,

Given

for checking account

6000=<x<10000 --> additional 100
10000=<x<14000 --> additional 300
14000=<x -->additonal 500

for savings account

8000=<x , 4% annual interest
8000>x , 3% annual interest

Now calculating for each combination

SA(Savings account)
CA(Checking account)

1. 14K SA + 6K CA

Interest on SA= 560
Additional Amount on CA=100
Total =660

2.12K SA + 8K CA

Interest on SA= 480
Additional Amount on CA=100
Total =580

3. 10K SA + 10K CA

Interest on SA= 400
Additional Amount on CA=300
Total =700

4. 8K SA + 12K CA

Interest on SA= 320
Additional Amount on CA=300
Total =620

5. 6K SA + 14K CA

Interest on SA= 180
Additional Amount on CA=500
Total =680

Therefore from all this , we can find the max interest earned in when 10K each is invested in savings account and checking account
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 02:02
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For this particular question, on taking the value of the checking account as 6000, we will have 20000-6000=14000 remaining. The return on both those investments calculated comes out to be:

6000*1.03+14000+500=20680

On taking the value of the checking account as 8000, we will have 20000-8000=12000 remaining. The return on both those investments calculated comes out to be:
8000*1.04+12000+300=20620

On taking the value of the checking account as 10000, we will have 20000-10000=10000 remaining. The return on both those investments calculated comes out to be:
10000*1.04+10000+300=20700 (Max value)

Hence the values of both the checking & savings account should be 10000 to maximize value for Hana
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 02:22
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To maximize Hana's year-end balance, we need to consider both the incentives for the checking account and the interest rate for the savings account. The total amount deposited is €20,000, which needs to be divided between the checking and savings accounts.

Given:
1. Checking Account Incentives:
- If deposited between €6,000 and €10,000, add €100.
- If deposited between €10,000 and €14,000, add €300.
- If deposited at least €14,000, add €500.

2. Savings Account Interest:
- If deposited at least €8,000, it earns 4% interest; otherwise, 3%.

Our goal is to select two amounts: one for the checking account and one for the savings account, such that the total year-end balance is maximized.

To maximize the total balance, let's analyze the possible combinations:

1. Checking Deposit: €14,000, Savings Deposit: €6,000
- Checking incentive: +€500 = €14,500
- Savings interest: 3% on €6,000 = €180
- Total balance: €14,500 + €6,180 = €20,680

2. Checking Deposit: €10,000, Savings Deposit: €10,000
- Checking incentive: +€300 = €10,300
- Savings interest: 4% on €10,000 = €400
- Total balance: €10,300 + €10,400 = €20,700

3. Checking Deposit: €12,000, Savings Deposit: €8,000
- Checking incentive: +€300 = €12,300
- Savings interest: 4% on €8,000 = €320
- Total balance: €12,300 + €8,320 = €20,620

Among these options, the combination that yields the highest total balance is:

- Checking Deposit: €10,000
- Savings Deposit: €10,000

The optimal combination for Hana's maximum year-end balance is: Checking Account: €10,000 and Savings Account: €10,000. This combination ensures Hana benefits from both incentives and interest to maximize her total balance of €20,700.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 02:35
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The correct answer is $14,000 in Checking Account and the remaining $6,000 in Savings Account.

This will maximise her returns because the CA will lead to a return of $500 and the SA will lead to a return of 3% i.e. $180, giving a total of $680. However, if we take another case of $12,000 in CA and $8,000 in SA, our returns would be $300 and $320 from CA and SA respectively (taking 4% interest from SA), giving a total of $620. This is less than the return earned in the previous case.
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Hana has decided to join a credit union, where she will open two accounts: a checking account and a savings account.

The credit union offers incentives to new checking account customers: If a customer deposits at least €6,000 but less than €10,000 into their checking account, the credit union will add an additional €100 to the initial checking account balance. If a customer deposits at least €10,000 but less than €14,000 into their checking account, the credit union will add an additional €300 to the initial checking account balance. If a customer deposits at least €14,000 into their checking account, the credit union will add an additional €500 to the initial checking account balance. Checking accounts do not earn any interest.

For new savings accounts with initial deposits of at least €8,000, the account earns interest at an annual rate of 4%. All other new savings accounts earn interest at an annual rate of 3%.

Hana will make an initial deposit at the beginning of the year totaling €20,000, distributed across both accounts such that her total year-end balance will be maximized. There will be no other transactions on either account for the entire year except for the incentives and interest income described above.

In the first column of the table, select the amount that Hana will deposit into the checking account. In the second column of the table, select the amount that Hana will deposit into the savings account. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 03:19
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Explanation

Hana wants to maximize her year-end balance by distributing €20,000 between a checking and a savings account.

  1. Checking Account Incentives:
    • €10,000 deposit earns a €300 bonus.
    • Depositing more (€14,000) gives a larger bonus (€500) but leaves only €6,000 for savings, which earns lower interest (3%).
  2. Savings Account Interest:
    • €10,000 deposit earns 4% (€400) interest.
    • Depositing less (€6,000) earns only 3% (€180).
By depositing €10,000 in both accounts:
  • Checking: €10,000 + €300 = €10,300
  • Savings: €10,000 + €400 = €10,400
  • Total Year-End Balance: €20,700
Final Answer:

[*]Checking Account: €10,000
[*]Savings Account: €10,000





[*]


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12 Days of Christmas GMAT Competition - Day 2: Hana has decided to 18 Dec 2024, 03:33
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If the customer deposits €6,000 into the checking account and €14,000 into the saving account, the total year-end balance will be \( 1.04*€14,000+€100+€6,000= €20,660\)

There is no need to calculate the total year-end balance in the end of the year, if the customer deposits €8,000 into the checking account. it will be definitely lower than that, when he deposits €6,000.

If the customer deposits €10,000 into the checking account and €14,000 into the saving account, the total year-end balance will be \( 1.04*€10,000+ €300+€10,000 = €20,700\)

No need to calculate for €12,000.

If the customer deposits €14,000 into the checking account and €6,000 into the saving account, the total year-end balance will be \(1.04*€6,000+€500+€14,000=€20,740\)

Answer: s €14,000 into the checking account and €6,000 into the saving account
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