Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 73.00. 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 73.0 when he fully retires, he will wants to have $2,751,668.00 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 6.00% interest rate.

Answer 1

Let x be the amount Derek contributes from his 26th birthday to 65th birthday. So, Future value of his contributions on his 65th birthday can be calculated by the formula of future value of annuity which is x*(((1+r)^n)-1)/r, Here r is 6% and n is 40 (from 26th to 65th). This gives 154.76x. Derek wants to have $2751668 one year after his 73rd birthday. So, after 9 years of his 65th birthday he needs $2751668. So, (154.76x)*(1.06)^9= 2751668. On solving, we get x= $10523.96

So, Derek needs to contribute an amount of $10523.96 from his 26th birthday to 65th birthday.