Question

Suppose you are going to receive $12,000 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?

C.	Suppose you plan to invest the payments for 6 years, what is the future value if the payments are an ordinary annuity?

D. Suppose you plan to invest the payments for 6 years, what is the future value if the payments are an annuity due?

Answer 1

a. Present Value of ordinary annuity:

We know that the ordinary annuity is when the payment is received at the end of the period thus for 6 years we will receive $ 12,000 at end of 1st year, 2nd year onwards

• Present Value = PMT x ((1 - (1 + r) ^ -n ) / r)

PMT = 12000

r = 11%

n = 6 years

Present Value = 12000 * ( ( 1- (1.11)^-6 /0.11))

= 50,766.45

b.

• Present Value of Annuity Due = PMT + PMT x ((1 - (1 + r) ^ -(n-1) / r)

In Annuity Due the amount is received at the begining of the period.

PMT = 12000

r = 11%

n = 6 years

Present Value = 12000 + 12000 * ( ( 1- (1.11)^-5 /0.11))

= 56,350.76

c. The Future value of Annuity is given by

Where C is amount received = 12000

i = Rate of interest = 11%

n = 6

FV = 12000 * ((1+0.11)^6 -1)/0.11

= 12000 * ((1.11)^6 - 1)/0.11

= 12000 * 7.9128595651

= 94,954.3147812

= 94,954.31

d. The future value of Annuity is given by

FV = 12000 *(((1.11)^6 -1)/0.11) * 1.11

= 12000 * 8.7832741173

= 105,399.289407132

= 105,399.29