Respuesta :
Answer:
Ans. Kurt can purchase a car up to $17,080.40
Explanation:
Hi, first we have to bring to present value this annuity of $300 per month, for that, we have to convert this effective annual rate of 7% to an effective monthly rate and finally, multiply by 12 the number of years in which Kurt plans to pay for the car, that is 48 months.
The rate is:
[tex]r(monthly)=(1+r(annual))^{\frac{1}{12} } -1=(1+0.07)^{\frac{1}{12} } -1=0.00565415[/tex]
Or 0.565415% effective monthly.
Now it is time to use the following equation to find the present value of a $300 annuity. After that, we have to add the down payment and that is the price of the car.
[tex]PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }[/tex]
[tex]PresentValue=\frac{300((1+0.00565415)^{48}-1) }{0.00565415(1+0.00565415)^{48} }[/tex]
[tex]Present Value=12,580.40[/tex]
Now the car price has to be the present value that we just found plus the down payment that Kurt is planning to make.
[tex]CarPrice=12,580.40+4,500=17,080.40[/tex]
Best of luck.
