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

The certain amount that is paid to but an annuity is usually equivalent to the present value of all the payments that is being made in the future at a discounted rate of return.

However; given that the annual installments begins from today; then the present values of the remaining 11 installments wiil be determined.

In addition to that; the payment of $120,000 covers the 12 installments. the present value of one installment is said to be $15,000

Thus; the present value of the remaining 11 installments is:

$120,000 - $15,000 = $105,000

We compute the rate of return using the RATE formula in EXCEL as shown below.

A B

1 Present value 120000

2 Time period 12 years

3 Number of payments

in future 11

4 Payment Amount 15000

5 Rate of Return = RATE (B3,B4. -(B1 - 15000))

The outcome of the result is as follows:

A B

1 Present value $120000

2 Time period $12 years

3 Number of payments

in future 11

4 Payment Amount $15000

5 Rate of Return 8.41%

∴ The rate of return that will be earned is 8.41%