Question

What is the value today of a money machine that will pay $4,683.00 every six months for 11.00 years? Assume the first payment is made 3.00 years from today and the interest rate is 9.00%.

Answer 1

Interest rate for 6 months = 9%/2 = 4.5% = 0.045

Number of payments = 11 * 2 = 22

First let's find the present value as of one period before the first payment, that is 2.5 years from now. Then we will discount that by 2.5 * 2 = 5 periods to get the present value today.

PV0 = PV2.5/(1 + r)^5

PV0 = 64,552.4611614867/(1 + 0.045)^5

PV0 = $51,800.1900132297

The value today of the money machine = $51,800.1900132297