9
QuizMultiple Choice

Exponential Equations in Financial Contexts — Quiz

Question 9 • Advanced Financial Algebra

An investment has an annual interest rate of 4.8% compounded daily. One investor starts with $⁢2,500 and will review the investment when it reaches $⁢2,886.38 Which equation can the investor use to find the number of years, t , it will take before the investment needs to be reviewed?

Answer
A
2 comma 500 is equal to 2 comma 886 point 3 8 times open paren 1 plus 0 point 0 4 8 over 365 close paren to the t th power
B
2 comma 500 is equal to 2 comma 886 point 3 8 times open paren 1 plus 0 point 0 4 8 over 365 close paren raised to the 365 t power
C
2 comma 886 point 3 8 is equal to 2 comma 500 times open paren 1 plus 0 point 0 4 8 over 365 close paren to the t th power
D
2 comma 886 point 3 8 is equal to 2 comma 500 times open paren 1 plus 0 point 0 4 8 over 365 close paren raised to the 365 t power

Explanation

Use the compound interest formula A = P(1 + r/n)^(nt), where P is the starting amount, A is the target amount, r is the annual rate, and n is the number of compounding periods per year. Here P = 2,500, A = 2,886.38, r = 0.048, and daily compounding means n = 365. Substituting gives 2,886.38 = 2,500(1 + 0.048/365)^(365t), which is choice D.

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