Question

How much do you need to invest every month in an annuity to

reach a goal of $25,000 at the end of 5 years, if compounding is

done every month and the annual interest rate is 4%. Round up

to the next penny.

Answer 1

A=25000 is the future value. P the value that we need to invest. r= 0.04 represent the interest rate in fraction. n = 12 represent the number of times that the rate is compounded in a year. t = 5 years.

If we solve for the value of P we got:

`P= (A)/((1+ (r)/(n))^(nt))`

And replacing we got:

`P= (25000)/((1+ (0.04)/(12))^(12*5)) =20475.078`

And rounded to the nesrest penny we need to invest $20475.08 in order to have after 5 years $25000

Explanation:

For this case we can use the future value with compound interest given by:

`A = P (1+ (r)/(n))^(nt)`

Where:

A=25000 is the future value. P the value that we need to invest. r= 0.04 represent the interest rate in fraction. n = 12 represent the number of times that the rate is compounded in a year. t = 5 years.

If we solve for the value of P we got:

`P= (A)/((1+ (r)/(n))^(nt))`

And replacing we got:

`P= (25000)/((1+ (0.04)/(12))^(12*5)) =20475.078`

And rounded to the nesrest penny we need to invest $20475.08 in order to have after 5 years $25000