Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 70.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 70.0 when he fully retires, he will wants to have $2,910,513.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 8.00% interest rate.

(add 1 to N)

Answer 1

Amount required to have in his retirement Account one year after the day he turns 70 = $2,910,513

So, amount required to have in his account at the time of retirement = $2,910,513 x PVIF @ 8% for 6 years

= $2,910,513 x 0.6302

= $1,834116.89

Calculation of contributions to his retirement account from his 26th birthday to his 65th birthday(i.e. 40 years)

No.of years (N) = 40

Rate of Return (I) = 8 %

Maturity Amount(P) = $1,834116.89

Annual Contribution =      

  

Hence, If he contributes $7079.99 every year for the next 40 years (i.e. rom his 26th birthday to his 65th birthday) at an interest rate of 8% he will get a maturity value of $1,834116.89 on his 65 th birthday. which will accumulated to $2,910,513 at end of one year after his 70th birthday.