Using technology, determine the present value given that you make monthly payments of $250.00 at 2.3% compounded monthly over a 5 year period. Round your answer to the nearest cent. a. $10,776.33 b. $8,046.04 c. $14,156.84 d. $14,165.26

Accepted Solution

Answer:The correct option is c.Step-by-step explanation:Given information: monthly payments = $250.00, Interest rate = 2.3% compounded monthly over a 5 year period.The formula for monthly payment:[tex]C=\frac{PV(\frac{r}{n})}{1-(1+\frac{r}{n})^{-n*t}}[/tex]Where, C is monthly payment, r is rate of interest, n is number of times interest compounded in a year, t is number of years, PV is present value.[tex]250=\frac{PV(\frac{0.023}{12})}{1-(1+\frac{0.023}{12})^{-12*5}}[/tex][tex]250=\frac{PV(\frac{0.023}{12})}{1-(1+\frac{0.023}{12})^{-60}}[/tex][tex]250(1-(1+\frac{0.023}{12})^{-60})=PV(\frac{0.023}{12})[/tex][tex]\frac{250(1-(1+\frac{0.023}{12})^{-60})}{(\frac{0.023}{12})}=PV[/tex][tex]14156.83566=PV[/tex][tex]14156.84\approx PV[/tex]The present value is 14156.84.Therefore the correct option is c.