A real estate investor wants to purchase a rental property that generates an annuity payment of $3,000 per month. If the interest rate is 6 percent, how much should the investor invest today to receive the desired monthly payment for the next 10 years? Round your answer to the nearest whole dollar.(1 point) Responses $180,225 $180,225 $350,650 $350,650 $270,220 $270,220 $250,125
First, we need to calculate the present value of an annuity formula to determine the amount the investor should invest today. The formula is:
PV = Pmt * [(1 - (1 + r)^(-n)) / r]
Where:
PV = present value (amount to invest today)
Pmt = payment per period ($3,000)
r = interest rate per period (6% or 0.06)
n = total number of periods (10 years * 12 months = 120 months)
Plugging in the values:
PV = $3,000 * [(1 - (1 + 0.06)^(-120)) / 0.06]
PV = $3,000 * [(1 - (1 + 0.06)^(-120)) / 0.06]
PV = $3,000 * [(1 - (1 + 0.06)^(-120)) / 0.06]
PV = $3,000 * [(1 - (1.06)^(-120)) / 0.06]
PV = $3,000 * [(1 - 0.13239) / 0.06]
PV = $3,000 * [0.86761 / 0.06]
PV = $3,000 * 14.46017
PV = $43,380.51
Therefore, the investor should invest $43,380.51 today to receive the desired monthly payment for the next 10 years. The closest whole dollar is $43,381.
None of the answer choices provided match the calculated value.