Your grandmother wishes to have a steady source of income for the first ten years of her retirement. She can buy an annuity which will pay her $6,000 per year at the end of each year for ten years. She will receive her first payment one year from today. Similar risk investments are yielding 7%. What should she pay for the investment?
A) $30,501
B) $42,141
C) $45,091
D) $60,000

Question

Quizplus · Accepted Answer

The value of the annuity can be calculated using the present value formula for an annuity: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PV is the present value of the annuity, PMT is the annual payment ($6,000), r is the annual interest rate (7% or 0.07), and n is the number of payments (10). Plugging in the values, we get $PV = 6000 \times \left(\frac{1 - (1 + 0.07)^{-10}}{0.07}\right)$, which calculates to approximately $42,141.

Your Grandmother Wishes to Have a Steady Source of Income