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)
- $180,225
- $350,650
- $270,220
- $250,125
To determine how much the investor should invest today to receive the desired monthly payment for the next 10 years, we can use the formula for the present value of an annuity:
PV = PMT * [1 - (1 + r)^(-n)] / r
where
PV = Present value
PMT = Annuity payment per month ($3,000)
r = Interest rate per month (6%/12 = 0.5% or 0.005)
n = Number of months (10 years * 12 months/year = 120 months)
Plugging in the values, we get:
PV = $3,000 * [1 - (1 + 0.005)^(-120)] / 0.005
PV = $3,000 * [1 - (1.005)^(-120)] / 0.005
PV = $3,000 * [1 - 0.464147] / 0.005
PV = $3,000 * 0.535853 / 0.005
PV = $320.56 / 0.005
PV = $64,112 expected investment now
Therefore, the investor should invest approximately $64,112 now to receive the desired monthly payment for the next 10 years. Since this option is not listed in the choices provided, none of the given options are correct.