What is present value of annuity?

Question

What is the present value (PV) of a 12-year lease arrangement with an interest rate of 7.5 percent that requires annual payments of $4,250 per year with the first payment being due now?

I got $32,874.93 BUT my work partner got $10,122.56

Who is right and why?

Answer 1

Neither got it totally right but the first one is closer. Ultimately the PV of an annuity with a finite time period n is the same as the sum of n individual present value calculations. One key thing is the first payment is due now. That's time period zero and there is no discount to it - that's where the first answer is off. On a calculator you can just identify the variables and it will give you the PV but below is longhand to show where everything comes from.

Yr 0 = 4250 Yr 6 = 2754 Total = 35,339

Yr 1 = 3953 Yr 7 = 2562

Yr 2 = 3677 Yr 8 = 2383

Yr 3 = 3421 Yr 9 = 2217

Yr 4 = 3182 Yr 10 = 2062

Yr 5 = 2960 Yr 11 = 1918