Claire deposited 2 dollars comma 500 into an account that accrues interest monthly. She made no additional deposits or withdrawals. After 2 years, Claire had 2 dollars comma 762 point 3 5 in the account. What is the annual interest rate of the account? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t is equal to years since initial deposit n is equal to number of times compounded per year r is equal to annual interest rate (as a decimal) cap p is equal to initial (principal) investment cap v times t is equal to value of investment after t years
Answer
A
11 percent
B
31 percent
C
26 percent
D
5 percent
Explanation
Use the compound interest formula with a principal of $2,500, 24 months, and an ending value of $2,762.35: 2,762.35 = 2,500(1 + r/12)^24. Dividing by 2,500 and solving gives r ≈ 0.05, or 5%. Therefore, the annual interest rate is 5 percent.
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Question

Claire deposited 2 dollars comma 500 into an account that accrues interest monthly. She made no additional deposits or withdrawals. After 2 years, Claire had 2 dollars comma 762 point 3 5 in the account. What is the annual interest rate of the account? Compound interest formula: cap v times t is equal to cap p times open paren 1 plus r over n close paren raised to the n t power t is equal to years since initial deposit n is equal to number of times compounded per year r is equal to annual interest rate (as a decimal) cap p is equal to initial (principal) investment cap v times t is equal to value of investment after t years

Answer

A

11 percent

B

31 percent

C

26 percent

D

5 percent

Explanation

Use the compound interest formula with a principal of $2,500, 24 months, and an ending value of $2,762.35: 2,762.35 = 2,500(1 + r/12)^24. Dividing by 2,500 and solving gives r ≈ 0.05, or 5%. Therefore, the annual interest rate is 5 percent.

AI-written and checked against the verified answer.

Revolt · Accepted Answer

5 percent

Modeling with Exponential and Logarithmic Equations — Quiz

Explanation

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