Question

You deposit X in an account today in order to fund your retirement. You would like to receive payments of 50 per year, in real terms, at the end of each year for a total of 12 years, with the first payment occurring seven years from now. The inflation rate will be 0.0% for the next 6 years and 1.2% per annum thereafter. The annual effective rate of return is 6.3%. Calculate X to the nearest dollar.

Answer 1

Amount to be received from retirement fund at the end of each year = $50 per year

Payment will start 7 years from now which means payment will start at the end of 7th year, while inflation during the first 6 years is nil while therafter it is 1.2% per annum.

Calculating the Present Value of Annuity payment at the end of 6 year using Present Value of Growing ordinary annuity formula:-

Where, C= Periodic Payments = $50

r = Periodic Interest rate = 6.3%

g = Inflation rate = 1.2%

n= no of periods = 12

PV6 = $436.93

So, Present Value of annuity payment at the end of 6th year is $436.93

Now, Calculating Present Value today using PV6:-

PV0 = PV6/(1+r)^n

PV6 = $436.93

r = Interest Rate = 0.063

n = no of years = 6

PV0 = $436.93/(1+0.063)^6

PV0 = $302.84

So, Amount need to be depsoited today is $303. hence, X is $303