Question

Jane is planning for her retirement. Each month she places $200 in an account that pays 12% nominal interest compounded monthly. She makes the first deposit of $200 on January 31, 1997. The last $200 deposit will be made on December 31, 2016. If the interest rate remains constant and all deposits are made as planned, what amount will be in Jane’s retirement account on January 1, 2017? Answer: $198,000.

I know the correct answer but am struggling to get it. Please explain each step in your solution. Will up vote.

Answer 1

Monthly payment = A = $200

Number of years = n = from 1997 to 2016 = 20

Number of months in a year = m = 12

Rate of interest = r = 0.12

Future value = FV =?

FV = [A / (r/m)] × [{1 + (r/m)}^(n×m) - 1]

      = [200 / (0.12/12)] × [{1 + (0.12/12)^(20 × 12) – 1]

      = [200 / 0.01] × [{1 + 0.01}^240 – 1]

      = 20,000 × (1.01^240 – 1)

      = 20,000 × (10.9 – 1)

      = 20,000 × 9.9

      = $198,000 (Answer)