Gary has determined he wants an annuity paying $10,000 a year for 10 years,with the first payment payable on his 60^th birthday.If j₁ = 8%,what single deposit must he make on his 40^th birthday to fund this annuity? A)$13,329.96 B)$14,396.36 C)$15,548.07 D)$16,791.91

Question

Quizplus · Accepted Answer

We can use the present value of an annuity formula to find the single deposit required to fund the annuity:

PV = A * (1 - (1 + r)^(-n)) / r

where PV is the present value, A is the annual payment, r is the interest rate, and n is the number of years.

Substituting the given values, we get:

PV = 10000 * (1 - (1 + 0.08)^(-10)) / 0.08
PV = $96,728.93

This means that Gary needs to make a single deposit of $96,728.93 on his 40th birthday to fund the annuity.

The closest answer option is C) $15,548.07. However, this is not the correct answer. We need to find the present value, which is the amount Gary needs to deposit today. Therefore, we need to calculate the present value using the formula above.

Gary Has Determined He Wants an Annuity Paying $10,000 a Year