Question

addison put a $2290 item on layaway by making a 20% down payment and agreeing to pay $230 a month. how many months sooner would she pay off the item if she increased her monthly payment to $310?

2 months sooner
6 months sooner
14 months sooner
8 months sooner

Answer 1

To calculate how many months Addison would pay off the item sooner by increasing her monthly payments, we need to determine both scenarios.

1. **Initial Details**:
- Item price: $2290
- Down payment: 20%
- Monthly payment initially: $230
- Monthly payment if increased: $310

2. **Calculating Down Payment**:
\[
\text{Down payment} = 20\% \text{ of } 2290 = 0.20 \times 2290 = 458
\]

3. **Calculating Remaining Balance**:
\[
\text{Remaining balance} = 2290 - 458 = 1832
\]

4. **Calculating Number of Months for $230 Payment**:
\[
\text{Months} = \frac{\text{Remaining balance}}{\text{Monthly payment}} = \frac{1832}{230} \approx 7.96 \text{ months}
\]
Since Addison can't pay for a fraction of a month, she would need 8 months to pay off the item at $230 per month.

5. **Calculating Number of Months for $310 Payment**:
\[
\text{Months} = \frac{\text{Remaining balance}}{\text{Monthly payment}} = \frac{1832}{310} \approx 5.9 \text{ months}
\]
Rounding up, she would need 6 months to pay off the item at $310 per month.

6. **Calculating the Difference**:
\[
\text{Months sooner} = 8 \text{ months} - 6 \text{ months} = 2 \text{ months}
\]

Therefore, if Addison increases her monthly payment to $310, she would pay off the item **2 months sooner**.

The answer is:
**2 months sooner**.