Question

Suppose you are going to receive $21,000 per year for 6 years. The appropriate interest rate is 11 percent.

a. What is the present value of the payments if they are in the form of an ordinary annuity?

b. What is the present value if the payments are an annuity due?

Answer 1

1. Present Value of Annuity = P * [( 1 - ( 1 +R)^-N] / R
P= Payment

R = rate per period

N = Number of period

= 21000 * [( 1 - ( 1 + 11%)^-6] / 11%

= 21000 * [( 1 - (1.11)^-6] / 0.11

= 21000 * [( 1 - 0.534640) / 0.11]

= 21000 * 4.230545

= 88841.445

So, The Present Value of Ordinary Annuity is 88841.445

B) In Case of annuity due, The payment is Made at the beginning of the period so the present value is Higher, It can be calculated as

Present Value of Annuity Due = Present Value of Ordinary annuity * ( 1 + Interest rate)

= 88841.445 * ( 1 + 11%)

= 98614.0039

Present value of ordianry annuity is 98614.0039