Question

How much would you pay today for this annuity? It will payout $740 each quarter for 20 years. Your desired annual interest return is  5.9 %. (Don't forget to adjust the interest rate for quarterly, in addition to the time period.)

a. $34,620.05

b. 30,102.01

c. 34,228.31

d. 31,972.27

e. 32,457.76

Thank you!!

Answer 1

Present Value of Ordinary Annuity/Annuity Regular

Present Value of an Ordinary Annuity is calculated by using the following formula

Present Value of an Ordinary Annuity = P x [{1 - (1 / (1 + r) n} / r]

Interest Rate (r) = 1.475% per Quarter [5.90% / 4 Quarters]

Number of Periods (n) = 80 Quarters [20 Years x 4 Quarter per year]

Quarterly Payments (P) = $740 per Quarter

Present Value of Ordinary Annuity = P x [{1 - (1 / (1 + r) ⁿ} / r]

= $740 x [{1 - (1 / (1 + 0.01475)⁸⁰} / 0.1475]

= $740 x [{1 - (1 / 3.22645)} / 0.01475]

= $740 x [{1 - 0.30994} / 0.01475]

= $740 x 46.78385

= $34,620.05

“Hence, The Present Value of this annuity today = $34,620.05”