Question

Today, you are purchasing a 15-year, 6.5 percent annuity at a cost of $36,500. The annuity will pay annual payments starting one year from today. What is the amount of each payment?

Answer 1

Answer:

Periodic payment = $3,881.88 (Approx).

Explanation:

Given:

Present value of annuity = $36,500

Rate = 6.5% = 0.065

Number of payment = 15

Computation:

$Present\ value\ of\ annuity = periodic\ payment[\frac{1-(1+r)^{-n}}{r} ]$

$36,500 = periodic\ payment[\frac{1-(1+0.065)^{-15}}{0.065} ]\\\\36,500 = periodic\ payment[\frac{1-(1.065)^{-15}}{0.065} ]\\\\36,500 = periodic\ payment[\frac{1-0.388826524}{0.065} ]\\\\36,500 = periodic\ payment[\frac{0.611173476}{0.065} ]\\\\36,500 = periodic\ payment[9.40266886 ]\\\\periodic\ payment = 3,881.87658$

Periodic payment = $3,881.88 (Approx).