Question

You put $500 per month in the bank today earning 6% per year. How much will be in the account in 5 years if the interest compounds annually? What if it compounds monthly?

Answer 1

Calculation of effective interest rate for the month
Annual rate = 6%
therefore equation will be
6% =(1+r)^12 -1
r =0.4867551%
Amount will be in 5 years
Future Value of an Ordinary Annuity
= C*[(1+i)^n-1]/i
Where,
C= Cash Flow per period =500
i = interest rate per period =0.4867551%
n=number of period =12*5 =60
= $500[ (1+0.004867551)^60 -1] /0.004867551
= $500[ (1.004867551)^60 -1] /0.004867551
= $500[ (1.3382 -1] /0.004867551]
= $34,742.89