Question

You are scheduled to receive annual payments of $11,100 for each of the next 24 years. Your discount rate is 10 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year

Answer 1

Answer:

The difference in the present value is $988.32.

Explanation:

The difference in the present value can be calculated using the following 3 steps:

Step 1: Calculation of the present value if you receive these payments at the beginning of each year

This can be calculated using the formula for calculating the present value (PV) of annuity due given as follows:

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

Where;

PVA = Present value if you receive these payments at the beginning of each year = ?

P = Annual payments = $11,100

r = interest rate = 10%, or 0.10

n = number of years = 24

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

PVA = $11,100 * ((1 - (1 / (1 + 0.10))^24) / 0.10) * (1 + 0.10)

PVA = $10,871.54

Step 2: Calculation of the present value if you receive these payments at the end of each year

This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PVO = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)

Where:

PVO = Present value if you receive these payments at the end of each year = ?

Other values are as defined in Step 1 above.

Substitute the values into equation (2), we have:

PVO = $11,100 * ((1 - (1 / (1 + 0.10))^24) / 0.10)

PVO = $9,883.22

Step 3: Calculation of the difference in the present value

This can be calculated as follows:

Difference in the present value = PVA - PVO = $10,871.54 - $9,883.22 = $988.32