Question

Doreen is celebrating her 35th birthday and decides she needs to start saving for retirement beginning at age 65. She wants to be able to withdraw 90,000 annually for 15 years starting on her 66th birthday. She intends to invest at 8% over the life of the account. Her employer will contribute 1500 per year until she retires. Additionally, she expects a 25,000 distribution from a family trust on her 55th birthday which will be deposited into the retirement account. what amount will she need to deposit annually to make the desired withdraws at retirement?

Answer 1

PV of all the withdrawls on her 65th birthday = A / r x [1 - (1 + r)^-n] = 90,000 / 8% x [1 - (1 + 8%)^-15] =  770,353.08

Let's say P is the amount she will need to deposit annually to make the desired withdraws at retirement. Hence, future value of this annuity (P + employer's contribution) + FV of the distribution from a family trust on her 65th birthday = PV of all the withdrawls on her 65th birthday = 770,353.08

Hence, (P + 1,500) / r x [(1 + r)^t - 1] + 25,000 x (1 + r)^{(65 - 55)}

= (P + 1,500) / 8% x [(1 + 8%)³⁰ - 1] + 25,000 x (1 + 8%)¹⁰

= 113.28 x (P + 1,500) + 53,973.12 = 770,353.08

Hence, P = (770,353.08 - 53,973.12) / 113.28 - 1,500 =  6,323.80 - 1,500 = $  4,823.80

Hence the required amount = P = $ 4,823.80