Question

1. How does an increase in interest rates affect the present value of a future payment?

2. How does an increase in the size of a future payment affect the present value of a future payment?

3. Two payments of $1,000 are to be made. One of them will be paid one year from today and the other will be paid two years from today. Which has the greater present value? Why?

Answer 1

(1)

Present value (PV) = Future value (FV) / (1 + r)^N where r: Interest rate, N: Number of periods

Therefore, ceteris paribus, the higher the value of r, the higher the value of [(1 + r)^N] and the lower the PV. So an increase in interest rate will decrease present value.

(2)

Using above formula, ceteris paribus, the higher (lower) the value of FV, the higher (lower) the present value. So an increase in future payment will increase present value.

(3)

Using above formula, ceteris paribus, the higher the value of N, the higher the value of [(1 + r)^N] and the lower the PV. So an increase in N will decrease present value. Hence, the payment made after 1 year will have higher PV than the payment made after 2 years.