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}*(1+(r)/(100))^t \\ =16000(1+(5)/(4*100))^(5*4) \\ =16000*(1+0.0125)^(20) \\ =16000*(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}*(1+(r)/(100))^t \\ =16000(1+(5)/(12*100))^(5*12) \\ =16000*(1+0.004167)^(60) \\ =16000*(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}*(1+(r)/(100))^t \\ =16000(1+(3)/(4*100))^(5*4) \\ =16000*(1+0.0075)^(20) \\ =16000*(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}*(1+(r)/(100))^t \\ =16000(1+(3)/(12*100))^(5*12) \\ =16000*(1+0.0025)^(60) \\ =16000*(1.0025)^(60) \\ =18585.87 \end{gathered}`

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