Question

Comprehensive Given:

current income $50,000

income needed in retirement $45,000

current age 35

age at retirement 70

age at death 90

investment return prior to retirement 7%

investment return during retirement 4%

a) Calculate the nest-egg needed at retirement. Assume the annual income amount will be taken at the beginning of each year during retirement.

b) How much must this individual save each year in order to meet the retirement-savings goal? Assume the individual will save an equal amount annually.

Answer 1

current income = $50,000

income needed in retirement , A1= $45,000

current age = 35

age at retirement = 70

age at death = 90

investment return prior to retirement = 7% = 0.07

investment return during retirement = 4%= 0.04

investment period for retirement income, T= 70 - 35 = 35

period between retirement and death = 90-70 = 20 years

a)

nest-egg needed at retirement = (A1*PVIFA ) + A1

PVIFA =present value interest factor of annuity ((1+R)^N-1-1)/((1+R)^N-1 * R) = ((1.04)¹⁹-1)/((1.04)¹⁹ * 0.04) = 13.1339394

nest-egg needed at retirement = (A1*PVIFA ) + A1 = (45000*13.1339394) + 45000 = $636027.272944 OR $636027.27 (rounding off to 2 decimal places)

b)

let amount to be saved annually = A2

A2 = nest-egg needed at retirement /FVIFA

FVIFA = future value interest factor of annuity = ((1+B)^T -1)/(B) = ((1.07)³⁵-1)/(0.07) = 138.2368784

A2 = 636027.272944/138.2368784 =$ 4600.995628 OR $4601.00 ( rounding off to two decimal places)