3
QuizMultiple Choice

Exponential Equations in Financial Contexts — Quiz

Question 3 • Advanced Financial Algebra

An investor is putting $⁢10,000 into a certificate of deposit. It compounds interest twice a year at a rate of 6 percent Which equation can the investor use to determine how long it will take to reach a balance of $⁢10,612.08 ?

Answer
A
10 comma 612 point 0 8 is equal to 10 comma 000 times open paren 1 plus 0 point 0 6 over 4 close paren raised to the 2 t power
B
10 comma 000 is equal to 10 comma 612 point 0 8 times open paren 1 plus 0 point 0 6 over 4 close paren to the t th power
C
10 comma 000 is equal to 10 comma 612 point 0 8 times open paren 1 plus 0 point 0 6 over 2 close paren raised to the 2 t power
D
10 comma 612 point 0 8 is equal to 10 comma 000 times open paren 1 plus 0 point 0 6 over 2 close paren raised to the 2 t power

Explanation

Use the compound-interest equation A = P(1 + r/n)^(nt), where P = 10,000, A = 10,612.08, r = 0.06, and n = 2 because interest compounds twice a year. Substituting gives 10,612.08 = 10,000(1 + 0.06/2)^(2t), which is choice D.

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