One of your customers has just made a purchase in the amount of $14,400. You have agreed to payments of $305 per month and will charge a monthly interest rate of .93 percent. How many months will it take for the account to be paid off?

To determine how many months it will take to pay off the account, we need to solve for the number of periods $N$ in the loan amortization formula. The formula for the present value of an ordinary annuity is:

\[
PV = PMT \times \left(\frac{1 - (1 + r)^{-N}}{r}\right)
\]

Where:
- $PV$ is the present value or the loan amount ($14,400).
- $PMT$ is the monthly payment amount ($305).
- $r$ is the monthly interest rate (0.93% or 0.0093).
- $N$ is the number of payments or months to solve for.

Rearranging the formula to solve for $N$:

\[
N = \frac{\log\left(\frac{PMT}{PMT - PV \times r}\right)}{\log(1 + r)}
\]

Let's calculate $N$.It will take approximately **63 months** to pay off the account, since the number of months must be rounded up to ensure the loan is fully paid off.

Would you like any further details, or do you have any questions?

### Related Questions:
1. What would be the total interest paid over the 63 months?
2. How would the number of months change if the monthly payment were increased?
3. What if the interest rate were reduced to 0.5% per month?
4. Can you calculate the monthly payment if the loan were to be paid off in exactly 50 months?
5. What if the loan amount were different, say $10,000 or $20,000?
6. How does a balloon payment affect the number of months required?
7. What is the effect of making an additional payment each month on the loan term?
8. How would switching to bi-weekly payments instead of monthly affect the loan duration?

### Tip:
When calculating the time required to pay off a loan, always consider rounding up the number of payments to ensure the loan is fully repaid.

Learn how to calculate the number of months required to pay off a $14,400 purchase with monthly payments of $305 at a 0.93% monthly interest rate. Detailed step-by-step solution included.

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