Question

You win the lottery and must decide how to take the payout. use an 8% discount rate. what is the present value of $10,000 a year received at the end of each of the next nine years? $45,000

Answer 1

For compounding interest, there is a formula relating the present worth (P) with the annuity (A). This is shown in the picture. The 'i' is the effective interest rate while n is the time. You should make sure that you are consistent with the units. If your time is in terms of years, your interest should be in terms of percent per year compounded yearly. Moreover, your annuity should be per yearly basis. In this case, it is already consistent so we don't need to convert. Substituting the values,

P = 10,000[(1.08^9-1)/(0.08*1.08^9)]
P = $62,468.88