13
QuizMultiple Choice

N/A — Exam

Question 13 • Financial Math

An investment compounds quarterly, or 4 times a year, and has a published annual interest rate of 3.4% The initial investment is $⁢8,000 Which equation can the investor use to find out how long it will take for the value to reach $⁢8.276⁢.28 ?

Answer
A
8 comma 276 point 2 8 is equal to 8 comma 000 times open paren 1 plus 0 point 0 3 4 over 4 close paren raised to the 4 t power
B
8 comma 276 point 2 8 is equal to 8 comma 000 times open paren 1 plus 0 point 0 1 2 over 4 close paren raised to the 16 t power
C
8 comma 000 is equal to 8 comma 276 point 2 8 times open paren 1 plus 0 point 0 1 2 over 4 close paren raised to the 16 t power
D
8 comma 000 is equal to 8 comma 276 point 2 8 times open paren 1 plus 0 point 0 3 4 over 4 close paren raised to the 4 t power

Explanation

Use the compound interest formula A = P(1 + r/n)^(nt), where P is the initial investment, r is the annual rate as a decimal, and n is the number of compounding periods per year. Substitute A = 8,276.28, P = 8,000, r = 0.034, and n = 4 to get 8,276.28 = 8,000(1 + 0.034/4)^(4t). This is choice C.

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