Question

A 15-year annuity pays $1,300 per month, and payments are made at the end of each month. The interest rate is 10 percent compounded monthly for the first six years and 8 percent compounded monthly thereafter. What is the present value of the annuity

Answer 1

Answer:

162075.97 dollars.

Explanation:

The time period of annuity = 15 years

Annuity amount = $1300 per month

The interest rate for the first six-year = 10%

Monthly interest rate = 10% / 12 = 0.83%

Thus number pf periods = 6 * 12 = 72  

Interest rate for another 9 years = 8%

Monthly interest rate = 8% / 12 = 0.67%

Number of period = 8 * 12 = 96

Use the below formula to find the present value of the annuity.

$\text{Present value of annuity} =\frac{A(1-(1+r)^{-n})}{r} \\\\= \frac{1300(1-(1+0.0083)^{-72})}{0.0083} + \frac{1300(1-(1+0.0067)^{-96})}{0.0067} \\= 162075.97 dollars.$