Question

ssume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. You need money today to open a new restaurant, and your uncle offers to give you $100,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment

Answer 1

13.08%

Step-by-step explanation:

this is an annuity due, and to determine its present value we can use the following formula:

present value = (annual payment / i) x {1 - [1 / (1 + i)ⁿ]} x (1 + i)

100,000 = (15,000 / i) x {1 - [1 / (1 + i)¹²]} x (1 + i)

The math is really complicated if you do it by hand, instead you should use a financial calculator. You would need to calculate the IRR, but the cash flows are:

first cash flow = -85,000

then 11 cash flows of 15,000 (remember that an annuity due is collected in advance)

IRR = 13.08%