Question

Your friend offers to pay you an annuity of $2,500 at the end of each year for 3 years in return for cash today. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Answer 1

Answer:

Annuity per period (A) = $2,500

Interest rate (r) = 5.5% = 0.055

Number of years (n) = 3 years

Present value (PV) = ?

The amount to be paid for the annuity

PV = A(1 + r)n - 1

             r

PV = $2,500(1 + 0.055)3 -  1

                       0.055

PV = $2,500(1.055)3 - 1

                       0.055

PV = $2,500(1.174241375 - 1)

                        0.055

PV = $2,500 x 3.168025

PV = $7,920.06

Explanation:

The present value of an annuity equals annuity per period multiplied by present value of annuity factor at 5.5% for 3 years. In this case, the annuity per period, interest rate and number of years were provided in the question with the exception of present value. The present value becomes the subject of the formula.                  

Answer 2

Based on the calculation below, the most that should be paid for the annuity is $6,744.83

How to calculate the present value of an ordinary annuity?

Since the annuity of $2,500 will be paid at the end of each year, the most that should be paid for the annuity can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value or the most you should pay for the annuity = ?

P = Annuity payment = $2,500

r = Interest rate on other investment = 5.5%, or 0.055

n = number of years = 3

Substitute the values into equation (1), we have:

PV = $2,500 * ((1 - (1 / (1 + 0.055))^3) / 0.055) = $6,744.83

Learn more about annuities here: https://brainly.com/question/13032788.

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