Question

You plan to retire in 21 years. You would like to maintain your current level of consumption which is $38,591 per year. You will need to have 25 years of consumption during your retirement. You can earn 5.6% per year (nominal terms) on your investments. In addition, you expect inflation to be 4.32% inflation per year, from now and through your retirement.

How much do you have to invest each year, starting next year, for 7 years, in real terms to just cover your retirement needs?

Answer 1

Years to retirement = 21

Current level of consumption = $38,591 per year

Inflation, i = 4.32% per year

Level of consumption at retirement = Current level of consumption*(1+inflation rate)^{years to retirement}

= $38,591*(1+4.32%)²¹ = $93,800.51

Years in Retirement = 25

Nominal return on investments, r = 5.6% per year

Inflation adjusted return = [(1+r)/(1+i)]-1 = [(1+5.6%)/(1+4.32%)]-1 = 1.226994%

Amount needed at retirement can be calculated using PV function in spreadsheet

PV(rate, number of periods, payment amount, future value, when-due)

Where, rate = inflation adjusted return = 1.226994%

number of periods = years in retirement = 25

payment amount = Level of consumption at retirement = $93,800.51

future value = 0

when-due = when is the consumption made each year = beginning = 1

Amount needed at retirement = PV(1.226994%, 25, 93800.51, 0, 1) = $2,033,607.70 --------------(1)

If you invest $1 each year in real terms, then you are increasing annual investment by the rate of inflation each year

The future value of these investments after 7 years can be calculated using the future value formula of a growing annuity

Where C = first payment = $1

r = annual rate of return = 5.6%

g = growth rate = inflation rate = 4.32%

n = investment period = 7 years

Future value of $1 invested in real terms for 7 years

FV = 78.125*0.119821 = $9.360988

Future value of this amount at retirement, FV_R = FV*(1+r)^t

Where r = annual rate of return = 5.6%

t = remaining years to retirement = 21-7 = 14 years

FV_R = $9.360988*(1+5.6%)¹⁴

= $9.360988*2.144346 = $20.073197

This is the value of $1 invested in real terms for 7 years at retirement. If instead of $1, amount A is invested

Future Value of A invested in real terms for 7 years at retirement = 20.073197A -----------------(2)

Equating (1) and (2)

20.073197A = $2,033,607.70

A = $2,033,607.70/20.073197 = $101,309.60

You would need to invest $101,309.60 each year, starting next year, for 7 years, in real terms to cover your retirement needs