Question

In: Finance

Your best friend Frank just celebrated his 30th birthday and wants to start saving for his...

Your best friend Frank just celebrated his 30th birthday and wants to start saving for his anticipated retirement. Frank plans to retire in 35 years and believes that he will have 20 good years of retirement and believes that if he can withdraw $90,000 at the end of each year, he can enjoy his retirement. Assume that a reasonable rate of interest for Frank for all scenarios presented below is 8% per year. This is an annual rate, review each individual question for more specifics on compounding periods per year.

1. If Frank decides to make monthly deposits for 35 to reach his same retirement goal, how much must Frank start depositing one month from today?

2. If Frank decides instead to take exotic vacations each year for the next 5 years, and delay putting aside funds for that time, (1st deposit at the end of 6 years from now, leaving only 30 years to grow his retirement nest egg), what amount must he deposit annually to be able to make the desired withdrawals at retirement?

Solutions

Expert Solution

1. Withdrawals required for 20 years = X = 90000 years

Interest Rate = r = 8%

Number of years = 30 years

Value required at end of 35 years to withdraw $90000 each year for 20 years = X/(1+r) + X/(1+r)2 + .... + X/(1+r)20 = X[1- (1+r)-n]/r = 90000[1- (1+0.08)-20]/0.08 = $883633.27

Let amount deposited each month be P

Monthly interest rate = r = 0.08/12

Number of periods = n = 35*12 = 420 months

Value after 35 years = P(1+r)n-1 +....+ P(1+r)2 + P(1+r) + P = P[(1+r)n -1]/r = P[(1+0.08/12)420 -1]/(0.08/12) = 2293.88P

This is equal to the amount required at 35 years

=> 2293.88P = 883633.27

=> P = $385.21

2.

Amount required at retirement to withdraw 90000 for 20 years = $883633.27

Let monthly deposited be P

Number of periods = n = 30 years

Value after 30 years = P(1+r)n-1 +....+ P(1+r)2 + P(1+r) + P = P[(1+r)n -1]/r = P[(1+0.08)30 -1]/0.08 = 113.28P

This is equal to the amount required at 35 years

=> 113.28P = 883633.27

=> P = $7800.43


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