Alva Thomas has decided to place $10,000 in an account payable to his alma matter when he dies. If the account grows at an annual rate of 6% compounded monthly and he lives for another 10 years, the university will receive
A) 10,000(1 + .06)10
B) 10,000(1 + .005)120
C) 10,000(1 + .06)120
D) 10,000/(1 + .005)120

Question

Quizplus · Accepted Answer

The correct formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. In this case, $P = 10,000$, $r = 0.06$ (6% annual interest rate), $n = 12$ (since the interest is compounded monthly), and $t = 10$ years. Therefore, the correct calculation is $10,000(1 + \frac{0.06}{12})^{12*10}$ or $10,000(1 + 0.005)^{120}$, which matches choice B.

Alva Thomas Has Decided to Place $10,000 in an Account