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18 Dec 2024, 04:00
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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.
If Hana deposit 10000 into the checking account, she will receive 300 as bonus. If she deposit 10000 in the savings account, she will receive an additional 10000*.04=400 as bonus.
In this way, she can maximize her profit most.
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.
If Hana deposit 10000 into the checking account, she will receive 300 as bonus. If she deposit 10000 in the savings account, she will receive an additional 10000*.04=400 as bonus.
In this way, she can maximize her profit most.
18 Dec 2024, 04:28
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The total year end balance should be maximum. This will happen when €10,000 is invested at 4% interest in savings account, which will yield €400. While, remaining €10,000 is invested in checking account, incentives yield €300. In this case, total added value will be €700, which comes out to be maximum for the available options.
Checking account - €10,000
Savings account - €10,000
Checking account - €10,000
Savings account - €10,000
18 Dec 2024, 05:15
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In TPA questions, it’s always better to form a strategy before solving. Well, this is a detailed, bulky question, so it’s better if we take notes on our notepad.
The stem tells us that;
For a checking account,
For a savings account,
Now we have to find a way to maximise her total year-end balance on an initial deposit of 20k.
In TPA and quant questions in general we should look if in any way we can use the options to our advantage.
To get a fair idea of what we need to do, let's start with a situation in which we distribute an equal amount of 10k in both the accounts.
TOTAL= 20700.
Repeating this process with all the options we'll see that the above option give us the maximum year end balance and hence is the answer to the question.
So we can fill 10,000 as the answer in both columns.
The stem tells us that;
For a checking account,
| DEPOSIT | AMOUNT ADDED |
| 6k<=deposit<10k | +100 |
| 10k<=deposit<14k | +300 |
| 14k<=deposit | +500 |
For a savings account,
| DEPOSIT | INTEREST RATE |
| 8k<=deposit | 4% |
| deposit<8k | 3% |
Now we have to find a way to maximise her total year-end balance on an initial deposit of 20k.
In TPA and quant questions in general we should look if in any way we can use the options to our advantage.
To get a fair idea of what we need to do, let's start with a situation in which we distribute an equal amount of 10k in both the accounts.
| SAVINGS ACCOUNT | CHECKING ACCOUNT |
| 10k+4% of 10k | 10k+300 |
| 10k+400 | 10k+300 |
| 10400 | 10300 |
TOTAL= 20700.
Repeating this process with all the options we'll see that the above option give us the maximum year end balance and hence is the answer to the question.
So we can fill 10,000 as the answer in both columns.
18 Dec 2024, 05:23
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If 10k is deposited in C.A , earnings = 300 and earnings from remaining 10k in S.A is 400. Giving a total of 700.
All other variations have lesser earnings. Eg:
If C.A = 12k , incentive= 300 & S.A = 8k, interest = 320. Total = 620
If C.A = 14k , incentive = 500 & S.A = 6k, interest = 180. Total = 680
All other variations have lesser earnings. Eg:
If C.A = 12k , incentive= 300 & S.A = 8k, interest = 320. Total = 620
If C.A = 14k , incentive = 500 & S.A = 6k, interest = 180. Total = 680
Bunuel
