Question

Compound Interest: Suppose $16,000 is invested in each account below. In each case find the amount of money in the account at the end of 5 years?

Answer 1

Given,

The principal amount is $16000.

The time period is 5 years.

a)The rate of interest is 5%.

The amount compounded quarterly is,

$\begin{gathered} \text{Amount}=\text{ principal}\times(1+\frac{r}{100})^t \\ =16000(1+\frac{5}{4\times100})^{5\times4} \\ =16000\times(1+0.0125)^{20} \\ =16000\times(1.0125)^{20} \\ =20512.60 \end{gathered}$

Hence, the amount compounded quarterly is $20512.60.

b)The rate of interest is 5%.

The amount compounded monthly is,

$\begin{gathered} \text{Amount}=\text{ principal}\times(1+\frac{r}{100})^t \\ =16000(1+\frac{5}{12\times100})^{5\times12} \\ =16000\times(1+0.004167)^{60} \\ =16000\times(1.004167)^{60} \\ =20533.74 \end{gathered}$

Hence, the amount compounded monthy is $20533.74.

c)The rate of interest is 3%.

The amount compounded quarterly is,

$\begin{gathered} \text{Amount}=\text{ principal}\times(1+\frac{r}{100})^t \\ =16000(1+\frac{3}{4\times100})^{5\times4} \\ =16000\times(1+0.0075)^{20} \\ =16000\times(1.0075)^{20} \\ =18,578.95 \end{gathered}$

Hence, the amount compounded quarterly is $18578.95.

d)The rate of interest is 3%.

The amount compounded monthly is,

$\begin{gathered} \text{Amount}=\text{ principal}\times(1+\frac{r}{100})^t \\ =16000(1+\frac{3}{12\times100})^{5\times12} \\ =16000\times(1+0.0025)^{60} \\ =16000\times(1.0025)^{60} \\ =18585.87 \end{gathered}$

Hence, the amount compounded monthy is $18,585.87.