Question

Find the future value$4013 invested for 9 years at 4.1% compounded quarterly.

Answer 1

We are to find the future value

The future value can be calculated using

`FV=PV(1+(r)/(100\alpha))^(n\alpha)`

From the given information

PV = $4013

r = 4.1

n = 9 years

Since the investment is compounded quarterly then

α = 4

By substituting these values we get

`FV=\text{ \$4013(1 }+(4.1)/(100(4)))^(9(4))`

Simplifying the equation we get

`\begin{gathered} FV=\text{ \$}4013(1\text{ }+(4.1)/(400))^(36) \\ FV=\text{ \$}4013(1\text{ }+0.01025)^(36) \\ FV=\text{ \$}4013(1.01025)^(36) \\ FV=\text{ \$}4013(1.44436) \\ FV=\text{\$}5793.17 \end{gathered}`

Therefore,

The Future Value is $5793.17