Personal Savings and Consumer Credit: Part Two — Test
Question 19 • Advanced Financial Algebra
An investor is putting $12,000 into a certificate of deposit that compounds interest quarterly, or 4 times a year. The rate is 2.4% , and the account balance at the end will be $12,438.53 Which equation can the investor use to determine the length of time for this investment?
Answer
A
12 comma 438 point 5 3 is equal to 12 comma 000 times open paren 1 plus 0 point 0 2 4 over 4 close paren to the t th power
B
12 comma 438 point 5 3 is equal to 12 comma 000 times open paren 1 plus 0 point 0 2 4 over 4 close paren raised to the 4 t power
C
12 comma 000 is equal to 12 comma 438 point 5 3 times open paren 1 plus 0 point 0 2 4 over 4 close paren raised to the 4 t power
D
12 comma 000 is equal to 12 comma 438 point 5 3 times open paren 1 plus 0 point 0 2 4 over 4 close paren to the t th power
Explanation
For quarterly compounding, use the formula A = P(1 + r/n)^(nt), where P is the starting amount and A is the ending balance. Here P = 12,000, r = 0.024, and n = 4, so the equation is 12,438.53 = 12,000(1 + 0.024/4)^(4t). Choice A matches this equation, with t representing the time in years.
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