# Jamal wants to invest $150 every month for 10 years. At the end of that time he would like to have $25000. At what annual interest rate, compounded monthly, does Jamal need to invest to reach...

Jamal wants to invest $150 every month for 10 years. At the end of that time he would like to have $25000.

At what annual interest rate, compounded monthly, does Jamal need to invest to reach his goal?

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### 2 Answers

This question is related to the future value of growing annuity. It is given by;

`FV = A((1+i)^n-1)/i`

FV = Future value of the time period n

A = Initial payment at n=1

i = compound rate

n = number of payment period considered

For the question;

FV = $25000

A = $150

n = 120 months

`FV = A((1+i)^n-1)/i`

`25000 = 150((1+i)^120-1)/i`

`(25000/150) = ((1+i)^120-1)/i`

For ease of calculation we can set `(1+i) = r`

Then ;

`(25000/150) = (r^120-1)/(r-1)`

No using a scientific calculator you can solve this.

It will give r as;

`r = 1.00525`

`i = 0.00525`

So the monthly interest rate `= 0.00525xx100`

Annual interest rate `= 0.00525xx100xx12 = 6.31%`

*So the annual interest rate would be 6.31%.*

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### User Comments

This question is related to the future value of growing annuity. It is given by;

FV = Future value of the time period n

A = Initial payment at n=1

i = compound rate

n = number of payment period considered

For the question;

FV = $25000

A = $150

n = 120 months

For ease of calculation we can set

Then ;

No using a scientific calculator you can solve this.

It will give r as;

So the monthly interest rate

Annual interest rate

*So the annual interest rate would be 6.31%.*