Solve the problem.
-Which of the two rates would yield the larger amount in 1 year: $9 \%$ compounded monthly or $9 \frac { 1 } { 4 } \%$ compounded annually?
A) $9 \%$ compounded monthly
B) $9 \frac { 1 } { 4 } \%$ compounded annually
C) They will yield the same amount.

Question

Quizplus · Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount, $P$ is the principal, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the time in years. For $9\%$ compounded monthly, $r = 0.09$, $n = 12$, and $t = 1$. For $9\frac{1}{4}\%$ compounded annually, $r = 0.0925$, $n = 1$, and $t = 1$. Calculating both, the $9\%$ compounded monthly yields a larger amount due to the effect of monthly compounding.

Solve the Problem 9%9 \%9% Compounded Monthly Or 914%9 \frac { 1 } { 4 } \%941​%

Solve the Problem $9 \%$ Compounded Monthly Or $9 \frac { 1 } { 4 } \%$