Question

Assume that you are 30 years old today, and that you are planning on retirement at age 65. You expect you will live for another 20 years after retirement. (A) (6 points) Suppose you forecast that you need to spend $300,000 at age 66 and the amount is expected to increase at a rate of 3% per year due to inflation. You can earn 8% annual interest rate on your savings. Therefore, the total amount you need to have at age 65 for your post-retirement spending is equal to $ (in unit) The value of r-g is % in your valuation formula. (B) (6 points) Suppose instead you want to have $3,000,000 at age 65 for your post- retirement spending. To save the amount, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and your contribution will increase at a rate of 5% per year. If the annual interest rate is 8%, then your contribution at your 31th birthday will be equal to $ . (in unit)

Answer 1

Question A:

Annual Withdrawl amount = $300,000

g = Growth rate = 3%

r = interesr rate = 8%

n = 20 years

Amount of Money at the age 65 = [P / (r-g)] * [ 1- ((1+g)/(1+r))^n]

= [$300,000 / (8%-3%)] * [1 - ((1+3%)/(1+8%))^20]

= $6,000,000 * [1 - 0.38749792777]

= $3,675,012.43338

Therefore, Amount of Money at the age 65 is $3,675,012.43

Thevalue of (r-g) = (8%-3%) = 5% in the valuation formula

Question B:

Amount of Money at the age 65 is $3,675,012.43

g = Growth rate = 5%

r = interesr rate = 8%

n = 31 to 65 years = 35 years

Let Contribution on 31st birthday = P

Amount of Money at the age 65 = P [ [(1+r)^n - (1+g)^n] / (r-g)

$3,675,012.43= P [[(1+8%)^35 - (1+5%)^35] / (8%-5%)]

$3,675,012.43 = P[ 14.7853442943 - 5.516015] / 0.03

$110,250.373 = P * 9.26932929

P = $11,894.1047

Contribution on 31st Birthday = $11,894.10