Question

A 15-year annuity pays $2,200 per month, and payments are made at the end of each month. If the interest rate is 10 percent compounded monthly for the first seven years, and 6 percent compounded monthly thereafter, what is the present value of the annuity

Answer 1

$215,895.24

Step-by-step explanation:

The present value of an annuity is the current value of future payments from an annuity, given a specified rate of return, or discount rate. The higher the discount rate, the lower the present value of the annuity

First find the present value of the last 8 years of payment:

PV after 7 years: 2200 * (p/a,6%/12,96 )

PV = 2200 * (1-(1+0.06/12)-96/(0.06/12)

PV = 2200 * 76.0952

PV = $167,409.48

Present value today discounted by 84 months at 10% compounded monthly PV = 167409.48/(1+0.10/12)84

PV = $83,374.57

PV of first 7 years of payment:

2200 * (p/a,10%/12,84 )

PV = 2200 * (1-(1+0.10/12)-84/(0.10/12)

PV = 2200 * 60.2367

PV = $132,520.67

Total Present value of the annuity = $83,374.57 + $132,520.67

Total Present value of the annuity = $215,895.24