Question

Salary: 110,000

Match: 3%

Expected Return: 7%

Years: 35

If you save 15% of your salary each year, how much money would you have when you turn 65, assuming you earn a 7% annual return on your investments?  

Annual Savings?

Total Amount at age 65?

During retirement, your return drops to 5% annually as you decide to invest more conservatively to protect your principal. How much could you spend each year and not have your money run out before age 95?

How does this breakdown each year?

Amount Saved by Age 65 (from question 1):
Year in Retirement	Withdrawal Amount
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

Answer 1

Annual Savings = 15% of 110000 = $16500

Rate of Return r = 7%

Number of Years investment made = t = 35 years

Amount after t years = X(1+r)^t-1 +....+ X(1+r)² + X(1+r) + X = X[(1+r)^t -1]/r

Hence, Amount at age 65 = 16500[(1+0.07)³⁵ -1]/0.07 = $2280908.50

Let the amount withdrawn each year be P

number of Years = n = 30 years

Rate of return = r = 5%

The Present Value (at age 65) of all the future payments = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r

This is equal to the value computed in the previous step (amount accrued after 35 years of savings)

=> P[1- (1+r)^-n]/r = 2280908.50

P[1- (1+0.05)^-30]/0.05 = 2280908.50

=> P = $148376.37