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17 Dec 2024, 09:00
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Checking Account: €10,000
Savings Account: €10,000
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
48% (02:56) correct
52%
(02:51)
wrong
based on 500
sessions
History
Date
Time
Result
Not Attempted Yet
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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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.
| Checking Account | Savings Account | |
| €6,000 | ||
| €8,000 | ||
| €10,000 | ||
| €12,000 | ||
| €14,000 |
ShowHide Answer
Official Answer
Checking Account: €10,000
Savings Account: €10,000
17 Dec 2024, 10:00
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Bunuel
Manhattan Prep Official Explanation:
Step 1: Understand the Prompt and Question
Glance at the answers. The numbers point to a Quant-based question. Further, the percentages in the prompt indicate that this is a Percents problem.
Next, read the entire prompt and jot down the given information on your scratch paper:
Sav
8K+, 4% int
else 3% int
20K deposit
Finally, the prompt notes that Hana deposits money so as to maximize her total year-end balance, making this a Max/Min problem.
Step 2: Plan your Approach
The multiple tiers of checking account incentives make this difficult to solve with algebra. The round, evenly-spaced answers point instead to Working Backwards as a possible solution.
Furthermore, of the available answers, it would only make sense for Hana to deposit €6,000, €10,000, or €14,000 into her checking account initially, because those are the minimum values needed to increase her checking account incentive. Depositing any additional money into her checking account beyond those values would require her to deposit less money into her savings account, resulting in a loss of interest and making it impossible to maximize her return. Test each of these three scenarios and see which one results in the maximum year-end balance.
Step 3: Solve the Problem
Create a table to track your work:
Since the deposit totals €20,000, the savings deposit must be €20,000 minus whatever was deposited into the checking account. Update the table:
Write the checking incentive for each tier in the table:
In the first two rows, Hana has deposited more than €8,000, so she earns 4% interest. In the last row, she has not, so she earns 3% interest. Calculate the savings interest in each row, using your calculator if you wish:
0.04 × 14,000 = 560
0.04 × 10,000 = 400
0.03 × 6,000 = 180
Update the table:
Finally, calculate Hana’s year-end balance by adding the values of the cells in each row, again using your calculator if you wish:
Hana’s year-end balance is maximized in the second row, the scenario where she deposits an initial €10,000 into each account.
The correct answer is €10,000 for the first column and €10,000 for the second column.
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General Discussion
Heix
Joined: 21 Feb 2024
Last visit: 30 Apr 2026
Posts: 468
Given Kudos: 63
Location: India
Concentration: Finance, Entrepreneurship
Schools: Ross MM "26 NUS Columbia '27
GMAT Focus 1: 485 Q76 V74 DI77 
GPA: 3.4
WE:Accounting (Finance)
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17 Dec 2024, 09:44
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If Hana deposits 10000 in checking account and 10000 in savings account her total year end balance will be maximized
as if we deposits 10000 in checking account we will get an additional 300 dollars
and if Hana deposits 10000 in savings account Hana will get 10000 x 4 x 1 /100 = 400
Therefore total = 700
if we take savings 6000 and checking 14000 total will be 680 which is less than 700
if we take savings 14000 and checking 6000 total will be 660 which is again less than 700
if we take saving 8000 and checking 12000 total will be 620 less than 700
savings 12000 and checking 8000 total = 580 less than 700
so the correct answer is checking 10000 and savings 10000
as if we deposits 10000 in checking account we will get an additional 300 dollars
and if Hana deposits 10000 in savings account Hana will get 10000 x 4 x 1 /100 = 400
Therefore total = 700
if we take savings 6000 and checking 14000 total will be 680 which is less than 700
if we take savings 14000 and checking 6000 total will be 660 which is again less than 700
if we take saving 8000 and checking 12000 total will be 620 less than 700
savings 12000 and checking 8000 total = 580 less than 700
so the correct answer is checking 10000 and savings 10000
