Question

When the interest is compounded quarterly, the amount $\left(A\right)$ is calculated by:
($P$ = Principal, $r$ = rate of interest, $n$ = time period)

• A. $A=P(1+\frac{4r}{100}{)}^{\frac{n}{4}}$
• B. $A=P(1+\frac{r}{100}{)}^n$
• C. $A=P(1+\frac{r}{400}{)}^{4n}$
• D. $A=P(1+\frac{\frac{r}{4}}{400}{)}^{\frac{1}{4n}}$

Answer 1

The correct option is C

$A=P(1+\frac{r}{400}{)}^{4n}$

Formula for finding amount when the principal undergoes compound interest: $A=P(1+\frac{r}{100}{)}^n$
Since compounding is done quarterly,
$A=P(1+\frac{\frac{r}{4}}{100}{)}^{4n}$
$A=P(1+\frac{r}{400}{)}^{4n}$