In order to accumulate enough money for a down payment on a

In order to accumulate enough money for a down payment on a house, a couple deposits $231 per month into an account paying 3% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 3 years?

What is the amount after 3 yaers?

Solution

Deposit amount= $ 231

1st month deposit will be remain in the account for 36 month (3 year)

Rate of interest = 3% per annum

=(3/12)% per month

Compund interest formulae= Principal amount* (1+r/n)^(n*t)

r= rate of interest per year

n= compound interval (Monthly=12)

T= no of year

Maturity amount of 1st month money at the end of 3rd year = 231 (1+3/1200)^36

same way for second month money at the end of 3rd year= 231 (1+3/1200)^35

Same way for the last month money at the end of 3rd year= 231 (1+3/1200)^1

By adding all

Total maturity value at the end of 3rd year of total investment= 231 *[(1.0025)^36+(1.0025)^35+...+(1.0025)^2+(1.0025)^1)

=231*37.7146= 8712

Total Maturity value= $ 8712