Question

Your uncle, in his will, left you the sum of $40,000/year forever with payments starting three years (Year 3) from today (Year 0). However, the news is even better. He has specified that the amount would grow at 2% per year after the first payment to offset inflation rate (i.e., the second payment would be $40,000 x (1 + 0.02)). With an APR of 3% compounded annually, what is the PV of the inheritance today?

Answer 1

Amount received starting at year 3 = 40000

growth rate constant therefter (g) =2%

interest rate (i) = 3%

Value of inheritance 1 year before starting of annuity (at t=2) = annuity starting at year 3/(interest rate - growth rate)

=40000/(3%-2%)

=4000000

This is value at time 2 or future value =4000000

number of years from today (n) =2

interest rate (i) =3%

present value = future value/(1+i)^n

=4000000/(1+3%)^2

=3770383.637

So present value of this inheritance today is $3770383.64