Question

You have just turned 25 years old, and accepted a job offer. Now you must decide how much money to put into your retirement plan. The plan works as follows: Every dollar in the plan earns 8% per year. You cannot make withdrawals until you retire on your 60 th birthday. After that, you can make withdrawals as you see fit. You estimate that to live comfortably in retirement, you will need $80,000 per year, starting at the end of the first year of retirement and ending on your 100th birthday.

a. How much saving on your 60th birthday so that you can afford to spend $80,000 per year till you are 100?

b. If you contribute the same amount to the plan at the end of every year that you work, how much do you need to contribute each year to fund you retirement?

c. If you can save 2% more per year until you retire, how much do you need to contribute the first year to fund your retirement?

Answer 1

Question a:

P = Annual Withdrawl = $80,000

r = interest rate = 8%

n = 100 - 60 = 40 years

Amount required at 60 = P * [1 - (1+r)^-n] / r

= $80,000 * [1 - (1+8%)^-40] / 8%

= $80,000 * 0.953969067 / 0.08

= $953,969.068

Therefore, amount required at $953,969.07

Question b:

r = interest rate = 8%

n = 60-25 = 35 years

Let P = Annual Savings

Amount required at 60 = $953,969.07

Amount required at 60 = P * [(1+r)^n - 1] / r

$953,969.07 = P * [(1+8%)^35 - 1] / 8%

$953,969.07 = P * 172.316804

P = $5,536.13489

Therefore, amount required to save each year is $5,536.13

Question c:

r = interest rate = 8%

g = growth rate = 2%

n = 60-25 = 35 years

Let P = First annual savings

Amount required at 60 = $953,969.07

Amount required at 60 = [P / (r-g)] * [(1+r)^n - (1+g)^n]

$953,969.07 = [P / (8% - 2%)] * [(1+8%)^35 - (1+2%)^35]

$57,238.1442 = P * $12.7854548

P = $4,476.81722

Therefore, first annual savings is $4,476.82