Question

What is the value today of a money machine that will pay $7,490.00 per year for 39.00 years? Assume the first payment is made today and that there are 39.0 total payments. The interest rate is 10.00%.

Answer 1

This question is similar to calculating value of annuity.

Here, we recieve a fixed amount $7,490 for 39 years.

The present value of an annuity is the cash value of all of your future annuity payments. The rate of return or discount rate is part of the calculation. An annuity's future payments are reduced based on the discount rate. Thus, the higher the discount rate, the lower the present value of the annuity.

However this question is a case of annuity due.

Difference between annuity due and annuity: An ordinary annuity makes payments at the end of each time period, while an annuity due makes them at the beginning. All else being equal, the annuity due will be worth more in the present.

PV of Annuity Due= (PMTx(1-1/(1+r)^n)/r)x(1+r)

where PMT = Dollar amount of each annuity amount

r = interest rate

n = Number of periods the payment will be made.

Here,

PMT = 7490

n = 39

r=10%

Using the above formula,

PV of Annuity Due= (7490*(1-1/(1+10%)^39)/10%)*(1+10%)

PV of Annuity Due = $80,387