Question

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?

Accepted Answer

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%.

Answer

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%.

Math

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...

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