Question

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 start a new business, and your uncle offers to give you $92,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment?

Answer 1

Function Arguments ? X RATE 1 1 Nper Pmt 15000 Pv -92000 Evo Type 11 = 12 = 15000 = -92000 = 0 1 = 1 = 0.154813448 Returns the interest rate per period of a loan or an investment. For example, use 6%/4 for quarterly payments at 6% APR. Type is a logical value: payment at the beginning of the period = 1; payment at the end of the period = 0 or omitted. Formula result = 15.48% Help on this function D OK Cancel

Hence, Rate of return is 15.48%

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Answer 2

SOLUTION :

Let the rate return be r (in decimals)

Annuity due is applicable here as first payment is paid today.

PV of annuity due ($15000 per year for 12 years at discount rate of r) is $92000.

So, 

92000 = 15000(1+ r)((1+r)^12 - 1)/(r(1+r)^12)

By trial and error :

r = rate of return on selling annuity at $92000 = 0.1548 = 15.48% (ANSWER).