1
QuizMultiple Choice

Modeling with Exponential and Logarithmic Equations — Quiz

Question 1 • Mathematics III

Jacques deposited 1 dollars comma 900 into an account that earns 4 percent interest compounded semiannually. After t years, Jacques has 3 dollars comma 875 point 7 9 in the account. Assuming he made no additional deposits or withdrawals, how long was the money in 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
9 years
B
36 years
C
2 years
D
18 years

Explanation

Use the compound interest formula with principal $1,900, annual rate 0.04, and 2 compounding periods per year: 3,875.79 = 1,900(1.02)^(2t). Dividing by 1,900 gives approximately 2.0399 = (1.02)^(2t), which is about 36 semiannual compounding periods. Since there are 2 periods per year, 36 ÷ 2 = 18 years, so the correct choice is 18 years.

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