Question

Find the present value of receiving $1000 per year for ten years beginning in year 12 until year 21, assuming an interest rate of 9%.

Answer 1

Annuity received (P) start at end of year 11 or beginning from year 12 = 1000

number of payment (n) =10

interest rate (i) =9%

Present value of annuity formula (at year 11 end)= (P*(1-(1/(1+i)^n))/i

=1000*(1-(1/(1+9%)^10))/9%

=6417.657701

This is value at end of year 11 or future value =6417.657701

number of years from today (n) =11

Present value today = Future value/(1+i)^n

=6417.657701/(1+9%)^11

=2487.053182

So present value of this annuity is $2487.05