Question

6-4       Find the present values of the following ordinary annuities:

1. PMT of $400 each year 5 years at a simple rate of 12 percent, compounded annually.
2. PMT of $200 each year for 10 years at a simple rate of 12 percent, compounded annually.
3. The annuities described in parts a and b have the same amount of money paid into them and both earn interest at the same simple rate, yet the present value of the annuity in part a is greater than the one in part b. Why does this occur?

Answer 1

Answer a.

PMT = $400
Period, N = 5
Interest Rate, I/Y = 12%

Using financial calculator:
I/Y = 12%
N = 5
PMT = 400
FV = 0

PV = -1441.91

Present Value = $1,441.91

Answer b.

PMT = $200
Period, N = 10
Interest Rate, I/Y = 12%

Using financial calculator:
I/Y = 12%
N = 10
PMT = 200
FV = 0

PV = -1130.04

Present Value = $1,130.04

Answer c.

The Present Value and period of annuity are inversely related to each other, so if the annuity has the higher period, then its present value will be lower.