Question

our father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $35,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 3%. He currently has $130,000 saved, and he expects to earn 10% annually on his savings. 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.

How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round your intermediate calculations. Round your answer to the nearest cent.

Answer 1

Rate of inflation is 3% = 0.03

First retirement income to have the same purchasing power as $ 35000 today is = $ 35000 x 1.03¹⁰ = $ 47037.07

Now he needs to receive this amount (constant) for 25 years starting from the beginning of day 1.

For this, we calculate the present value of an annuity due as in =PV(rate,nper,pmt,fv,type) in excel

Syntax

=PV (rate, nper, pmt, [fv], [type])

Arguments

• rate - The interest rate per period.
• nper - The total number of payment periods.
• pmt - The payment made each period.
• fv - [optional] A cash balance you want to attain after the last payment is made. If omitted, assumed to be zero.
• type - [optional] When payments are due. 0 = end of period, 1 = beginning of period. Default is 0.

here rate = 10% = 0.1, nper =25, pmt = $ 47037.07, future value fv = 0 and type =1

Funds required at the time of retirement = PV(0.1,25,47037.07,0,1) = $ 469653.10

Syntax

=FV (rate, nper, pmt, [pv], [type])

Arguments

• rate - The interest rate per period.
• nper - The total number of payment periods.
• pmt - The payment made each period. Must be entered as a negative number.
• pv - [optional] The present value of future payments. If omitted, assumed to be zero. Must be entered as a negative number.
• type - [optional] When payments are due. 0 = end of period, 1 = beginning of period. Default is 0.

here rate = 10% = 0.1, nper = 10, pmt = 0, future value pv = $ 130000, and type = 0

The $ 130,000 already saved will grow to = FV(0.1,10,0,130000,0) = $ 337186.52

Funds required at the time of retirement = PV(0.1,25,47037.07,0,1) = $ 469653.10

The $ 130,000 already saved will grow to = FV(0.1,10,0,130000,0) = $ 337186.52

Funds needed = $ 469653.10 - $ 337186.52 = $ 132466.60

Annual savings required =PMT(rate,nper,pv,fv,type) = PMT(0.1,10,0,132466.60,0)

Syntax

=NPER (rate, pmt, pv, [fv], [type])

Arguments

• rate - The interest rate per period.
• pmt - The payment made each period.
• pv - The present value, or total value of all payments now.
• fv - [optional] The future value, or a cash balance you want after the last payment is made. Defaults to 0.
• type - [optional] When payments are due. 0 = end of period. 1 = beginning of period. Default is 0.

Annual savings required =PMT(rate,nper,pv,fv,type) = PMT(0.1,10,0,132466.60,0) = $ 8311.67 = $ 8311.70 (rounded to thee nearest cent)