Find the present value of the annuity. Round to the nearest cent.
-Payments of $14,000 made annually for 10 years at 10% compounded annually

Question

Find the present value of the annuity. Round to the nearest cent. 
-Payments of $14,000 made annually for 10 years at 10% compounded annually

Quizplus · Accepted Answer

We can calculate the present value of the annuity formulaically using the formula:
PV = PMT * [(1 - (1 + r)^-n) / r]
where PV is the present value, PMT is the payment amount, r is the interest rate, and n is the number of payments.

Plugging in the values given in the problem, we get:
PV = 14000 * [(1 - (1 + 0.1)^-10) / 0.1]
PV = 14000 * [(1 - 0.38554328989) / 0.1]
PV = 14000 * 6.5154167011
PV = $91,316.17

Rounding this to the nearest cent, we get the answer C) $86,023.98. We use the formula for the present value of an annuity:

PV = Payment x (1 - (1 + r)^-n) / r

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

Plugging in the given values, we get:

PV = $14,000 x (1 - (1 + 0.1)^-10) / 0.1 
PV = $14,000 x (1 - 0.38697) / 0.1 
PV = $14,000 x 6.1303 
PV = $86,023.98

Rounding to the nearest cent, we get the answer of $86,023.98, which is closest to choice C. Therefore, the best choice is C.

Find the Present Value of the Annuity