With a monthly annuity payment of $175, a 12 percent APR, and a payment plan spanning 5 years, what is the present value of the annuity? Round your answer to the nearest hundredth.
To calculate the present value of the annuity, we can use the formula for the present value of an annuity:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value of the annuity
PMT = Monthly annuity payment ($175)
r = Monthly interest rate (APR / 12 = 0.12 / 12 = 0.01)
n = Number of payments (5 years * 12 months/year = 60 payments)
Plugging in the values:
PV = $175 * [(1 - (1 + 0.01)^-60) / 0.01]
PV = $175 * [(1 - (1.01)^-60) / 0.01]
PV = $175 * [(1 - 0.54703134793) / 0.01]
PV = $175 * [0.45296865207 / 0.01]
PV = $175 * 45.296865207
PV = $7924.15
Therefore, the present value of the annuity, given a monthly annuity payment of $175, a 12 percent APR, and a payment plan spanning 5 years, is $7924.15.