To determine which monthly payment will allow Pete to pay off his [tex]$1800 balance the fastest, we will calculate how many months it would take for each of the given monthly payments. We will use the formula:
\[
\text{Months required} = \frac{\text{Total Balance}}{\text{Monthly Payment}}
\]
Here's the step-by-step calculation for each of the given options:
1. Option A: $[/tex]40 per month
[tex]\[
\text{Months required} = \frac{1800}{40} = 45
\][/tex]
2. Option B: [tex]$80 per month
\[
\text{Months required} = \frac{1800}{80} = 22.5
\]
Since Pete can't make a half payment, we round up to the next whole number of months. So, it will take 23 months.
3. Option C: $[/tex]50 per month
[tex]\[
\text{Months required} = \frac{1800}{50} = 36
\][/tex]
4. Option D: [tex]$60 per month
\[
\text{Months required} = \frac{1800}{60} = 30
\]
Summarizing our results:
- $[/tex]40 per month: 45 months
- [tex]$80 per month: 23 months
- $[/tex]50 per month: 36 months
- [tex]$60 per month: 30 months
From these calculations, the payment plan that will allow Pete to pay off his balance the fastest is with a monthly payment of $[/tex]80. Therefore, the choice is:
B. $80
