Question

Porsha calculates the amount of money she will have at the end of 6 years on a $5,000 investment earning 3.75% interest compounded quarterly. She writes the following expression:
5,000 (1 + 0.0375) superscript 24
Which of the following statements about Porsha's expression is true?
a.
Porsha's expression is correct.
b.
Porsha's expression should have 1 + 0.009375 in the parentheses.
c.
Porsha's expression should have an exponent of 6, not 24.
d.
Porsha's expression should have both 1 + 0.009375 in the parentheses and an exponent of 6.

Answer 1

Answer: b.

For quarterly compounding use A = P(1 + r/n)^{nt}. Here r = 0.0375, n = 4, t = 6, so the factor is 1 + 0.0375/4 = 1 + 0.009375 and the exponent is 4·6 = 24. Porsha's exponent 24 is correct but the parenthesis should be 1 + 0.009375.