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Jeremiah invests his savings of $120,000 by dividing it

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Jeremiah invests his savings of $120,000 by dividing it

by AAPL » Tue Mar 19, 2019 5:20 am

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Jeremiah invests his savings of $120,000 by dividing it between two interest-earning accounts. He puts 3/4 of his savings in an account that earns lower interest and 1/4 of his savings in an account that earns higher interest. He has no other accounts that earn interest and he makes $3,636 in interest by the end of the year. If one account earns 2 percent annual interest, and both accounts are compounded semiannually, what percent interest does the other account earn?

A. 3
B. 4
C. 5
D. 6
E. 7

OA D
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by GMATGuruNY » Thu Mar 21, 2019 3:05 am
AAPL wrote:Manhattan Prep

Jeremiah invests his savings of $120,000 by dividing it between two interest-earning accounts. He puts 3/4 of his savings in an account that earns lower interest and 1/4 of his savings in an account that earns higher interest. He has no other accounts that earn interest and he makes $3,636 in interest by the end of the year. If one account earns 2 percent annual interest, and both accounts are compounded semiannually, what percent interest does the other account earn?

A. 3
B. 4
C. 5
D. 6
E. 7
On the GMAT, compounded interest is typically just a bit more than simple interest.

Since the answer choices are all greater than 2% -- the percentage given in the prompt -- they must represent the HIGHER interest rate, with 2% representing the LOWER interest rate.

Lower rate:
Since 3/4 of the savings earn the lower 2% rate. we get:
(3/4 )(120,000) = 90,000 at the lower rate, implying $30,000 at the higher rate.
Since the 2% lower rate is compounded semi-annually, we get:
Interest earned = a bit more than 2% of 90,000 = a bit more than $1800.

Higher rate:
Interest earned at the higher rate = (total earnings) - (amount earned at the lower rate) ≈ 3636-1800 = 1836.
We can PLUG IN THE ANSWERS, which represent the higher rate.
When the correct answer is applied to the remaining $30,000, a bit more than $1800 in interest will be earned.

D: 6%, compounded semi-annually
Here, the interest earned = a bit more than 6% of 30,000 = a bit more than 1800.
Success!

The correct answer is D.
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by Scott@TargetTestPrep » Thu Mar 21, 2019 4:39 pm
AAPL wrote:Manhattan Prep

Jeremiah invests his savings of $120,000 by dividing it between two interest-earning accounts. He puts 3/4 of his savings in an account that earns lower interest and 1/4 of his savings in an account that earns higher interest. He has no other accounts that earn interest and he makes $3,636 in interest by the end of the year. If one account earns 2 percent annual interest, and both accounts are compounded semiannually, what percent interest does the other account earn?

A. 3
B. 4
C. 5
D. 6
E. 7

OA D

Since all the answer choices are greater than 2, we can see that the account that earns 2 percent annual interest is the one that earns the lower interest (let's call it account A), and thus it has 120,000 x 3/4 = $90,000 (before earning any interest). And the one that earns higher interest (let's call it account B) has $30,000 (before earning any interest).

Since the interest is compounded semiannually, account A will earn:

90,000 x 0.01 = $900 for the first half of the year, and

(90,000 + 900) x 0.01 = 90,900 x 0.01 = $909 for the second half of the year.

So the total amount of interest account A earns is 900 + 909 = $1809. That means account B earns 3636 - 1809 = $1827. We see that account B only has 1/3 of the amount of account A, yet it earns about the same amount in interest. It must mean that the interest rate of account B must be 3 times that of account A; that is, account B must be earning 6 percent annual interest. Let's verify that's the case:

If account B earns 6 percent annual interest, it will earn:

30,000 x 0.03 = $900 for the first half of the year, and

(30,000 + 900) x 0.03 = 30,900 x 0.03 = $927 for the second half of the year.

So the total amount of interest account B earns is 900 + 927 = $1827, which is exactly the amount of interest it earns for the year. So its interest rate must be 6 percent.

Answer: D

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by Scott@TargetTestPrep » Thu Mar 21, 2019 4:39 pm
AAPL wrote:Manhattan Prep

Jeremiah invests his savings of $120,000 by dividing it between two interest-earning accounts. He puts 3/4 of his savings in an account that earns lower interest and 1/4 of his savings in an account that earns higher interest. He has no other accounts that earn interest and he makes $3,636 in interest by the end of the year. If one account earns 2 percent annual interest, and both accounts are compounded semiannually, what percent interest does the other account earn?

A. 3
B. 4
C. 5
D. 6
E. 7

OA D

Since all the answer choices are greater than 2, we can see that the account that earns 2 percent annual interest is the one that earns the lower interest (let's call it account A), and thus it has 120,000 x 3/4 = $90,000 (before earning any interest). And the one that earns higher interest (let's call it account B) has $30,000 (before earning any interest).

Since the interest is compounded semiannually, account A will earn:

90,000 x 0.01 = $900 for the first half of the year, and

(90,000 + 900) x 0.01 = 90,900 x 0.01 = $909 for the second half of the year.

So the total amount of interest account A earns is 900 + 909 = $1809. That means account B earns 3636 - 1809 = $1827. We see that account B only has 1/3 of the amount of account A, yet it earns about the same amount in interest. It must mean that the interest rate of account B must be 3 times that of account A; that is, account B must be earning 6 percent annual interest. Let's verify that's the case:

If account B earns 6 percent annual interest, it will earn:

30,000 x 0.03 = $900 for the first half of the year, and

(30,000 + 900) x 0.03 = 30,900 x 0.03 = $927 for the second half of the year.

So the total amount of interest account B earns is 900 + 927 = $1827, which is exactly the amount of interest it earns for the year. So its interest rate must be 6 percent.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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