You deposit $200 each month into an account earning 3% interest compounded monthly.

Question

You deposit $200 each month into an account earning 3% interest compounded monthly. How much will you have in the account in 30 years?

Answer 1

First we need to figure out the period interest rate, i. We use the formula: i=r/m, where r is the nominal interest rate and m is the number of compounding periods. If the bank pays 3% compounded monthly, that means that the nominal annual interest rate is 3.0% and the monthly period interest rate is 3/12=0.25%. 

 

Now, we can use the uniform series compound-amount factor to find the future value. The equation is simply

F= A[((1+i)^n)-1]/i, where F is the future value, A is the annuity amount, i is the period interest rate.

F= 200[((1+0.0025)^(12*30))-1]/0.025

F= 200[(1.0025^360)-1]/0.025

F=200[2.4568-1]/0.025=200[1.4568/0.0025]

F=200*582.72= $116,544

 

One easy way to check if you are in the right ballpark is to just take 200*360 months= 72,000. You know that with interest payments, you should be getting MORE than 72,000 after 30 years.