Question

A 14-year annuity pays $2,600 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.

Required:

What is the present value of the annuity?

Answer 1

Annuity monthly payment = $2,600

Interest Rate for First 6 years = 10%

Divide this annuity in to 2 parts,

Interest Rate for First 6 years = 10%

After 6 years,

Time to maturity = 96 months

Monthly Payment = $2,600

Interest Rate = 8%

Using TVM calculation,

PV = [FV = 0, T = 96, I = 8%, PMT = 2600]

PV = $183,919

For the first 6 years,

Time to maturity = 72 months,

Monthly Payment = $2,600

Value at the end of 6 years = $183,919

Interest Rate = 10%

Using TVM calculation,

PV = [FV = 183919, T = 72, I = 10%, PMT = 2600]

PV = $241,532.68