Question

1. Assume that you are 24 years old today, and that you are planning on retiring at age 65. Your salary is expected to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 25^th birthday and will be 10% of your salary of $50,000 at that time. You plan to put aside 10% of your salary each year until you reach age 65. (Your last contribution will be made at your 65^th birthday.) Starting from your retirement date (your 65^th birthday), you will begin equal annual withdrawals to pay for your living expenses. You expect to die one day before your 101st birthday. (So your first withdrawal will happen on your 65^th birthday and your last on your 100^th birthday) How much money can you spend in each of your golden years of retirement? Assume discount rate for all cash flows is 7%. .Describe the processes

Answer 1

P = First Contribution = $50,000 * 10% = $5,000

n = 65- 24 = 41 years

g = growth rate = 5%

r = discount rate = 7%

Amount available in the retirement account at 65 = [P / (r-g)] * [(1+r)^n - (1+g)^n]

= [$5,000 / (7%-5%)] * [(1+7%)^41 - (1+5%)^41]

= $250,000 * [16.0226699 - 7.39198815]

= $250,000 * 8.63068175

= $2,157,670.44

PV = Amount available at retirement = $2,157,670.44

n1 = 65-100 = 36 withdrawals

Let P = Annual withdrawal amount

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

P + [P * [1 - (1+7%)^-(36-1)] / 7%] = $2,157,670.44

P + [P * 0.906337061 / 0.07] = $2,157,670.44

P + 12.9476723 P = $2,157,670.44

13.9476723 P = $2,157,670.44

P = $154,697.529

Therefore, Annual withdrawal amount during retirement is $154,697.53