Question

27. 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 begin to make annual withdrawals of $189,025.00 from his retirement account until he turns 89.00. 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 4.00% interest rate.

Answer 1

The annuity from received per year one year after 70 = 189,025.00
Number of years = 19
Rate = 4%
Value of all Annuity at age 70 = Annuity*(1-(1+r)^-n)/r = 189,025 *(1-(1+4%)^-19)/4% = 2,482,642.89

PV of retirement fund at age 65 =  2,482,642.89/(1+4%)⁵ = 2,040,551.49

Number of years of contributions in account = 40 years
Contributions per years = 2,040,551.49/((1+r)ⁿ -1)/r = 2,040,551.49/((1+4%)⁴⁰ -1)/4% = 21,473.72

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