Question

Assume that your father is now 50 years old, plans to retire in 10 years, and expects to live for 25 years after he retires - that is, until age 85. He wants his first retirement payment to have the same purchasing power at the time he retires as $50,000 has today. He wants all his subsequent retirement payments to be equal to his first retirement payment. (Do not let the retirement payments grow with inflation: Your father realizes that if inflation occurs the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then receive 24 additional annual payments. Inflation is expected to be 3% per year from today forward. He currently has $25,000 saved and expects to earn a return on his savings of 4% per year with annual compounding. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below. Open spreadsheet How much must he save during each of the next 10 years (with equal deposits being made at the end of each year, beginning a year from today) to meet his retirement goal? (Note: Neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity.) Do not round intermediate calculations. Round your answer to the nearest dollar. $ 97072.90

Answer 1

Retirement income needed in current Dollar terms= $50,000

Inflation rate=3%

Time to retire=10 years

Therefore, retirement income needed every year= $50,000*(1+3%)^10 = $67,195.82

Retirement income stream consist of an annuity due. Value of this annuity, on the date of retirement is $1,091,727.99 calculated using PV function of Excel as follows:

C6 f =PV(C1,C2,C3,C4,C5)*-1 1 Interest rate 2 Number of payments 3 Amount of periodical payments 4 Future value 5 Timing of payments in advance) 6 Present vlue 7 Rate Nper Pmt Fv 4.00% 25 $67,195.82 Type PV $1,091,727.99

Current savings=$25,000

Amount to be saved every year (at the end of the year), apart from the current savings, to meet the retirement goal, is $87,848.78 calculated using the PMT function of Excel as follows:

10 C6 - fo=PMT(C1,C2,C3,C4,C5)*-1 А. B 1 Interest rate Rate 4% 2 Number of deposits Nper 3 Present Value PV ($25,000.00) 4 Future value Fv $1,091,727.99 5 Timing of deposit (End of year) Type 6 Amount of yearly savings PMT | $87,848.78 7