In: Finance
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?
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