Vince has $35,000 to purchase an annuity that will provide him with payments of $1,000 at the end of every three months. If the funds earn 8% compounded quarterly, how long will the payments continue?

Question

Quizplus · Accepted Answer

To find the duration of the annuity, we use the formula for the present value of an ordinary annuity: $ P = \frac{R \times (1 - (1 + i)^{-n})}{i} $, where $ P $ is the present value, $ R $ is the regular payment, $ i $ is the interest rate per period, and $ n $ is the number of periods. Here, $ P = 35,000 $, $ R = 1,000 $, and $ i = 0.08/4 = 0.02 $. Solving for $ n $, we find that the payments will continue for 60 periods, which is equivalent to 15 years (since payments are made quarterly).

Vince Has $35,000 to Purchase an Annuity That Will Provide