Answer to Question #135121 in Financial Math for jaya

Question

An annuity is payable in arrear for 20 years. The first payment is of amount $8000 and the
amount of each subsequence payment decreases by $300 each year. Find the present value
of the annuity on the basis of an interest rate of 5% per annum.

Answer 1

Cash flows will reduce by $300 every year and will be discounted at 5%.

Present value of annuity = 8,000 / (1.05)¹ + 7,700 / (1.05)² + 7,400 / (1.05)³ + 7,100 / (1.05)⁴ + 6,800 / (1.05)⁵ + 6,500 / (1.05)⁶ +

6,200 / (1.05)⁷ + 5,900 / (1.05)⁸ + 5,600 / (1.05)⁹ + 5,300 / (1.05)¹⁰ + 5,000 / (1.05)¹¹ + 4,700 / (1.05)¹² + 4,400 / (1.05)¹³ + 4,100/(1.05)¹⁴

+ 3,800 / (1.05)¹⁵ + 3,500 / (1.05)¹⁶ + 3,200 / (1.05)¹⁷ + 2,900 / (1.05)¹⁸ + 2,600 / (1.05)¹⁹ + 2,300 / (1.05)²⁰

Present value of annuity = $70,151.16