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
