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A 13-year annuity pays $1,100 per month, and payments are made at the end of each...

A 13-year annuity pays $1,100 per month, and payments are made at the end of each month. The interest rate is 9 percent compounded monthly for the first five years and 6 percent compounded monthly thereafter.

What is the present value of the annuity?

Expert Solution

first we need to find the present value of $1,100 annuity for the remaining 7 years.

Rate = 6% / 12 = 0.5%

Number of periods = 8 * 12 = 96

Present value at year 5 = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value at year 5 = 1,100 * [1 - 1 / (1 + 0.005)⁹⁶] / 0.005

Present value at year 5 = 1,100 * 76.095218

Present value at year 5 = $83,704.74008

Rate = 9% / 12 = 0.75%

Number of periods = 5 * 12 = 60

Present value = Future value / (1 + r)ⁿ

Present value today = 83,704.74008 / (1 + 0.0075)⁶⁰

Present value today = 83,704.74008 / 1.565681

Present value today = $53,462.19318

Present value of annuity = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value of annuity = 1,100 * [1 - 1 / (1 + 0.0075)⁶⁰] / 0.0075

Present value of annuity = 1,100 * 48.173374

Present value of annuity = $52,990.71087

Total present value of the annuity = $52,990.71087 + $53,462.19318

Total present value of the annuity = $106,452.90

jeff jeffy answered 2 years ago

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