SATMathematics Practice Test 1

Questions 57 and 58 refer to the following information.

Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was

\$100

, and she uses the expression

\$100(x)^t

to find the value of the account after

t

years.

Question : 58 of 58

Marks: +1, -0

Jessica’s friend Tyshaun found an account that earns 2.5 percent interest compounded annually.
Tyshaun made an initial deposit of 100 into this account at the same time Jessica made a deposit of $100 into her account. After 10 years, how much more money will Tyshaun’s initial deposit have earned than Jessica’s initial deposit? (Round your answer to the nearest cent and ignore the dollar sign when gridding your response.)

Your Answer:

Validate

Solution:

Jessica made an initial deposit of 100 into her account.
The interest on her account is 2 percent compounded annually, so after 10 years, the value of her initial deposit has been multiplied 10 times by the factor

1+0.02=1.02

.
Hence, after 10 years, Jessica’s deposit is worth

100(1.02)10=121.899

to the nearest tenth of a cent.
Tyshaun made an initial deposit of 100 into his account.
The interest on his account is 2.5 percent compounded annually, so after 10 years, the value of his initial deposit has been multiplied 10 times by the factor

1+0.025=1.025

.
Hence, after 10 years, Tyshaun’s deposit is worth

100(1.025)^10=128.008

to the nearest tenth of a cent.
Hence, Jessica’s initial deposit earned 21.899 and Tyshaun’s initial deposit earned 28.008.
Therefore, to the nearest cent, Tyshaun’s initial deposit earned 6.11 more than Jessica’s initial deposit.

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