Question

An individual is 49 years old. At the end of each​ month, he deposits $350 in a retirement account that pays 5.37​%

interest compounded monthly.

​(a) After 9 years, what is the value of the​ account?

​(b) If no further deposits or withdrawals are made to the​ account, what is the value of the account when the individual reaches age​ 65?

Answer 1

(a) Amount deposited at end of each month = P = $350

Interest rate = r = 5.37% = 0.0537/12 monthly

Number of deposits made = n = 9*12 = 108

Hence, Value at end of 9 years = FV =  P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P

= P[(1+r)ⁿ -1]/r

= 350[(1+0.0537/12)¹⁰⁸ -1]/(0.0537/12)

= 48465.73

(b) No deposits are made till age 65

Number of years till ager 65 = 7 years

Number of months = n = 7*12 = 84

Hence, Value after 7 years = FV(1+r)ⁿ = 48465.73(1+0.0537/12)⁸⁴ = $70521.55