Question

Frank, who turns 40 today, will deposit $2,500 in his empty retirement account at the end of every three months, with the first deposit coming three months from now and the final deposit coming on his 50th birthday. There are no other withdrawals or deposits. The nominal interest rate convertible quarterly, is 10%. Find Frank’s account balance on his 57th birthday.

Answer 1

Given the nominal Interest rate is 10%

Note - We take this rate as annual nominal interest rate. Now let us calculate quarterly interest rate.

Let X be the quarterly interest

(1+X)⁴ = 1.1

Hence X = 0.024114 = 2.4114% approx

Let us calculate the future value of annuity for the next 10 years

Formula for future value of annuity is as follows.

P*((1+r)ⁿ - 1)/r

P = Equalised periodic payments.

r = rate on interest

n = Number of Periods

= 2500 * ((1.024114)⁴⁰-1)/0.024114 = 2500 * 66.09331 = $165233.3

Balance at the end of 50years - $165233.3

Compounding this balance for next 7 years. Then (165233.3)*(1.1)⁷ = $321993.

Hence the balance at the end of year 57 is $3,21,993.