Answer:
Present value (PV) of the annuity = $156,988.13
Explanation:
Since the payments are made at the end of each month, the formula for calculating the present value of an ordinary annuity is the relevant to use as follows:
PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)
Where for the first 5 years;
PV = Present value of the payments today =?
P = monthly payment = $1,700
r = monthly interest rate = 12%/12 = 1%, or 0.01
n = number of months = 5* 12 = 60
Substitute the values into equation (1) to have:
PV = 1,700 × [{1 - [1 ÷ (1+0.01)]^60} ÷ 0.01] = $76,423.57
Where for the last 5 years;
PV = Present value of the payments today =?
P = monthly payment = $1,700
r = monthly interest rate = 8%/12 = 0.67%
, or 0.0067
n = number of months = 5* 12 = 60
Substitute the values into equation (1) to have:
PV_5 = 1,700 × [{1 - [1 ÷ (1+0.0067)]^60} ÷ 0.0067] = $83,841.34
PV after five years is:
PV = $83,841.34 ÷ (1 + 0.0067)^6 = $80,564.57
PV of the annuity = $76,423.57 + $80,564.57 = $156,988.13
