To determine from which of the four stores Tom should purchase his washing machine, we need to find out which store offers the lowest monthly payment over the 18-month payment period, given the different prices and APRs. We will use the formula for fixed monthly payments:
[tex]\[ M = \frac{P \times r(1+r)^n}{(1+r)^n - 1} \][/tex]
where:
- [tex]\( M \)[/tex] is the monthly payment
- [tex]\( P \)[/tex] is the price of the washing machine
- [tex]\( r \)[/tex] is the monthly interest rate (APR divided by 12)
- [tex]\( n \)[/tex] is the number of months
Let's calculate the monthly payment for each store:
1. Bob's Nuts and Bolts:
- Price, [tex]\( P \)[/tex] = \[tex]$450.00
- APR = 21%, monthly \( r = \frac{21}{100 \times 12} = 0.0175 \)
Substituting into the formula:
\[
M = \frac{450 \times 0.0175 \times (1+0.0175)^{18}}{(1+0.0175)^{18} - 1}
\]
2. Steve's Scratch and Dent:
- Price, \( P \) = \$[/tex]405.00
- APR = 22%, monthly [tex]\( r = \frac{22}{100 \times 12} = 0.0183333 \)[/tex]
Substituting into the formula:
[tex]\[
M = \frac{405 \times 0.0183333 \times (1+0.0183333)^{18}}{(1+0.0183333)^{18} - 1}
\][/tex]
3. Wally's Washing Machines:
- Price, [tex]\( P \)[/tex] = \[tex]$432.00
- APR = 19%, monthly \( r = \frac{19}{100 \times 12} = 0.0158333 \)
Substituting into the formula:
\[
M = \frac{432 \times 0.0158333 \times (1+0.0158333)^{18}}{(1+0.0158333)^{18} - 1}
\]
4. Al's Appliances:
- Price, \( P \) = \$[/tex]475.00
- APR = 16%, monthly [tex]\( r = \frac{16}{100 \times 12} = 0.0133333 \)[/tex]
Substituting into the formula:
[tex]\[
M = \frac{475 \times 0.0133333 \times (1+0.0133333)^{18}}{(1+0.0133333)^{18} - 1}
\][/tex]
After calculating these monthly payments (using the given numerical result), the store with the lowest monthly payment is found to be:
b. Steve's Scratch and Dent
Tom should purchase his washing machine from Steve's Scratch and Dent to minimize his monthly payment.
