Question

A 15-year annuity pays $1,650 per month, and payments are made at the end of each month. If the interest rate is 10 percent compounded monthly for the first seven years, and 6 percent compounded monthly thereafter, what is the present value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The present value of the annuity is $161,951.17

Step-by-step explanation:

Annual Interest for 7 years = 10%

Monthly Interest = 10% /12 = 0.833%

Annual Interest for next 8 years = 6%

Monthly Interest = 6%/12 = 0.5%

Present Value = 1,650/1.00833 + 1650/1.008333^2 + ... + 1650/1.00833^84 + [1650/1.005 + 1650/1.005^2 + ... + 1650/1.005^96]*(1/1.00833^84)

Present Value = [1650*(1-(1/1.00833)^84)/0.00833] + [1650*(1-(1/1.005)^96)/0.005]*(1/1.00833^84)

Present Value = $161,951.17

Therefore, The present value of the annuity is $161,951.17.