tom is in dire need of a new washing machine. he knows what model he would like to get, but doesnt have the…

tom is in dire need of a new washing machine. he knows what model he would like to get, but doesnt have the cash to pay for it. he plans to get a line of credit (credit card) at the store when he purchases his new washer. he found four different stores that carry the same washing machine for different prices. the lines of credit they offer also come with different aprs. toms primary goal is to minimize his monthly payment as he pays the washing machine off over the next 18 months. from which of the four stores should tom purchase his washing machine?\n\n| store | price ($) | credit card apr |\n|--|--|--|\n| bobs nuts and bolts | $450.00 | 21% |\n| steves scratch and dent | $405.00 | 22% |\n| wallys washing machines | $432.00 | 19% |\n| als appliances | $475.00 | 16% |

tom is in dire need of a new washing machine. he knows what model he would like to get, but doesnt have the cash to pay for it. he plans to get a line of credit (credit card) at the store when he purchases his new washer. he found four different stores that carry the same washing machine for different prices. the lines of credit they offer also come with different aprs. toms primary goal is to minimize his monthly payment as he pays the washing machine off over the next 18 months. from which of the four stores should tom purchase his washing machine?\n\n| store | price ($) | credit card apr |\n|--|--|--|\n| bobs nuts and bolts | $450.00 | 21% |\n| steves scratch and dent | $405.00 | 22% |\n| wallys washing machines | $432.00 | 19% |\n| als appliances | $475.00 | 16% |

Answer

Explanation:

Step1: Recall the monthly - payment formula

The formula for the monthly payment of a loan is $M = P\frac{r(1 + r)^n}{(1 + r)^n-1}$, where $M$ is the monthly payment, $P$ is the principal amount (price of the washing - machine), $r$ is the monthly interest rate ($r=\frac{APR}{12}$), and $n$ is the number of payments. Here, $n = 18$.

Step2: Calculate the monthly payment for Bob's Nuts and Bolts

$P_1=450$, $APR_1 = 0.21$, so $r_1=\frac{0.21}{12}=0.0175$. $M_1 = 450\times\frac{0.0175(1 + 0.0175)^{18}}{(1 + 0.0175)^{18}-1}$ First, calculate $(1 + 0.0175)^{18}\approx1.3679$. $M_1 = 450\times\frac{0.0175\times1.3679}{1.3679 - 1}=450\times\frac{0.023938}{0.3679}\approx29.17$.

Step3: Calculate the monthly payment for Steve's Scratch and Dent

$P_2 = 405$, $APR_2=0.22$, so $r_2=\frac{0.22}{12}\approx0.01833$. $(1 + 0.01833)^{18}\approx1.3877$. $M_2 = 405\times\frac{0.01833\times1.3877}{1.3877 - 1}=405\times\frac{0.025436}{0.3877}\approx26.57$.

Step4: Calculate the monthly payment for Wally's Washing Machines

$P_3 = 432$, $APR_3 = 0.19$, so $r_3=\frac{0.19}{12}\approx0.01583$. $(1 + 0.01583)^{18}\approx1.3277$. $M_3 = 432\times\frac{0.01583\times1.3277}{1.3277 - 1}=432\times\frac{0.021018}{0.3277}\approx27.77$.

Step5: Calculate the monthly payment for Al's Appliances

$P_4 = 475$, $APR_4 = 0.16$, so $r_4=\frac{0.16}{12}\approx0.01333$. $(1 + 0.01333)^{18}\approx1.2677$. $M_4 = 475\times\frac{0.01333\times1.2677}{1.2677 - 1}=475\times\frac{0.016818}{0.2677}\approx29.67$.

Answer:

Steve's Scratch and Dent