suppose that you are thinking about buying a car and have narrowed down your choices to two options. the new…

suppose that you are thinking about buying a car and have narrowed down your choices to two options. the new - car option: the new car costs $29,000 and can be financed with a five - year loan at 7.44%. the used - car option: a three - year old model of the same car costs $15,000 and can be financed with a four - year loan at 7.52%. what is the difference in monthly payments between financing the new car and financing the used car? use pmt = p(r/n)/1-(1 + r/n)^(-nt). the difference in monthly payments between financing the new car and financing the used car is $ (round to the nearest cent as needed.)

suppose that you are thinking about buying a car and have narrowed down your choices to two options. the new - car option: the new car costs $29,000 and can be financed with a five - year loan at 7.44%. the used - car option: a three - year old model of the same car costs $15,000 and can be financed with a four - year loan at 7.52%. what is the difference in monthly payments between financing the new car and financing the used car? use pmt = p(r/n)/1-(1 + r/n)^(-nt). the difference in monthly payments between financing the new car and financing the used car is $ (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Calculate new - car monthly payment

For the new - car: $P = 29000$, $r=0.0744$ (annual interest rate), $n = 12$ (monthly payments), $t = 5$ years. First, calculate the exponent $-nt=-12\times5=-60$. The monthly payment formula is $PMT_{new}=\frac{29000\times(\frac{0.0744}{12})}{1-(1 +\frac{0.0744}{12})^{-60}}$. $PMT_{new}=\frac{29000\times0.0062}{1-(1 + 0.0062)^{-60}}$. Let $x=(1 + 0.0062)^{-60}\approx0.6977$. $PMT_{new}=\frac{179.8}{1 - 0.6977}=\frac{179.8}{0.3023}\approx594.77$.

Step2: Calculate used - car monthly payment

For the used - car: $P = 15000$, $r = 0.0752$ (annual interest rate), $n = 12$ (monthly payments), $t = 4$ years. First, calculate the exponent $-nt=-12\times4=-48$. The monthly payment formula is $PMT_{used}=\frac{15000\times(\frac{0.0752}{12})}{1-(1+\frac{0.0752}{12})^{-48}}$. $PMT_{used}=\frac{15000\times0.006267}{1-(1 + 0.006267)^{-48}}$. Let $y=(1 + 0.006267)^{-48}\approx0.7477$. $PMT_{used}=\frac{94.005}{1 - 0.7477}=\frac{94.005}{0.2523}\approx372.6$.

Step3: Calculate the difference

$Difference=PMT_{new}-PMT_{used}=594.77 - 372.6 = 222.17$.

Answer:

$222.17$