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? T T T Arial 3 (12pt) T- 5 - - - @i's Path:p Words:0

Please show work, thanks!

Answer 1

Please find the solution in the below images-

Note: Since we can not solve a higher degree equation, I have used hit and trial method to find the value of r.

39 Rate of retern that uncle would earn on this investment is equal to (6) So, Amount that unde offerd (invest now) $92,000 and it should be equal to the present value of the sum of future cash floud of annuity. 92,000 = 15,000 + 15,000 15,000 (ltr) (1+r) Et. .. +15,000 Cashflows $15.000 $1500 92000 = 15000 it I t (ltr) (+) (m ) 92,000 = 15, 92,000 5 15,500 [G 92,000 15,000 (1-(1tr32) Citro] (or using Hit & trial method, as we can not solve deghe equation, r= 15.45 to such high approx.

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).