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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

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Answer:

The rate of return that will be earned is 8.41%

Explanation:

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%

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