Question

You are saving to buy a car, and you deposit $200 at the end of each month for two years at an APR of 2.4% compounded monthly. What is the future value for this savings arrangement? That is, how much money will you have for the purchase of the car after two years? (Round your answer to the nearest cent.)

Answer 1

You are saving to buy a car

You save $200 at the end of each month

The present, P = $200

At the rate of 2.4% compounded monthly,

Rate of return, r, will be

`r=((2.4)/(100))/(12)=(0.024)/(12)=0.002`

Rate of return, r = 0.002

The deposit is made at the end of every month for 2 years,

Number of periods, n, will be

`n=2\text{ }*12=24`

The formula to find the present value is

`FV=P\lbrack((1+r)^n-1)/(r)\rbrack`

Substiute the values into the formula

`\begin{gathered} FV=200\lbrack((1+0.002)^(24)-1)/(0.002)\rbrack \\ FV=200\lbrack((1.002)^(24)-1)/(0.002)\rbrack \\ FV=200\lbrack(0.049120363)/(0.002)\rbrack \\ FV=200(24.56) \\ FV=\text{ \$4912} \end{gathered}`

Hence, the future value is $4,912