Question

A 15-year annuity pays $1,000 per month, and payments are made at the end of each month. The interest rate is 15 percent compounded monthly for the first six years and 14 percent compounded monthly thereafter.

  

What is the present value of the annuity?

Multiple Choice

• $108,515.59

• $72,323.18

• $867,878.16

• $70,876.72

• $73,769.64

Answer 1

Step 1: Present value (PV) of the first 6 years payments

Monthly interest rate for the first 6 years, r1 = 15%/12 = 0.0125

r1 = 0.0125

n = 6 * 12 = 72

PMT = 1,000

Step 2: Monthly interest rate for the next 9 years, r1 = 14%/12 = 0.01166666667

n = 9 * 12 = 108

This gives the present value at the end of 6 years

Now, let's discount this to today's value

PV = 61,223.1110396505/(1 + r1)^72

PV = 61,223.1110396505/(1 + 0.0125)^72

PV = $25,030.7059625969

Step 3: Add the results from step 1 and step 2

Present value of the annuity, PV = 47,292.474312 + 25,030.7059625969

PV = $72,323.1802745969

Option B is correct: $72,323.18