Assume 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 $120,000 for the annuity.If you sell it, what rate of return would your uncle earn on his investment?
A) 6.85%
B) 7.21%
C) 7.59%
D) 7.99%
E) 8.41%

Question

Quizplus · Accepted Answer

The rate of return your uncle would earn on his investment can be found using the present value of an annuity formula, which is PV = PMT × [(1 - (1 + r)^-n) / r], where PV is the present value, PMT is the payment per period, r is the rate per period, and n is the number of periods. Since the payment is made at the beginning of the period, this is an annuity due. The formula needs to be adjusted slightly or a financial calculator or software that can handle annuity due calculations should be used. Given that the uncle is paying $120,000 for the annuity, and the payments are $15,000 per year for 12 years, we need to find the rate that satisfies this equation. Without going through the complex algebra, using a financial calculator or software designed for these calculations, inputting these values would give us the closest rate to match the present value of $120,000. The correct answer is 8.41%, which indicates that at this rate, the present value of the annuity payments equals the $120,000 offered by the uncle.

Assume That You Own an Annuity That Will Pay You