Question

Find the present value of a ten-year annuity which pays $600 at the beginning of each quarter for the first 6 years, and then $500 at the beginning of each quarter for the remain years. The annual effective interest rate is 6%. Round your answer to two decimal places. 19865.60 x

Answer 1

Quarterly interest rate = (1 + Effective annual rate)^(1/4) - 1
Quarterly interest rate = (1 + 0.06)^(1/4) - 1
Quarterly interest rate = 1.01467 - 1
Quarterly interest rate = 0.01467 or 1.467%

Quarterly payment for first 6 years = $600
Quarterly payment for next 4 years = $500

Payments are made at the beginning of each year

Present value = $600 + $600/1.01467 + … + $600/1.01467^22 + $600/1.01467^23 + $500/1.01467^24 + $500/1.01467^25 + … + $500/1.01467^38 + $500/1.01467^39
Present value = $600 * 1.01467 * (1 - (1/1.01467)^24) / 0.01467 + $500 * 1.01467 * (1 - (1/1.01467)^16) / 0.01467
Present value = $600 * 20.402359 + $500 * 14.376795
Present value = $19,429.81