With a monthly annuity payment of $150, a 14 percent APR, and a payment plan spanning 5 years, what is the present value of the annuity? Round your answer to the nearest hundredth.(1 point) Responses $5,225.24 $5,225.24 $7,326.67 $7,326.67 $4,325.15 $4,325.15 $6,446.55
To calculate the present value of an annuity, we can use the formula:
PV = PMT x [(1 - (1 + r)^-n) / r]
where:
PV = Present Value
PMT = Periodic payment (monthly annuity payment)
r = Periodic interest rate (APR / number of compounding periods per year)
n = Total number of payments
Given that the monthly annuity payment is $150, the APR is 14%, the payment plan spans 5 years (60 months), the formula becomes:
PV = $150 x [(1 - (1 + 0.14/12)^-60) / (0.14/12)]
Calculating the present value:
PV = $150 x [(1 - (1 + 0.01166667)^-60) / (0.01166667)]
PV = $150 x [(1 - 0.189688) / 0.01166667]
PV = $150 x (0.810312 / 0.01166667)
PV = $150 x 69.375406
PV = $10,406.31
Rounded to the nearest hundredth:
PV = $10,406.31
Therefore, the present value of the annuity is $10,406.31.