Fill in the blanks. In the forumula below (?) is the regular payment amount required to repay a loan of (?) dollars paid (?) times per year over (?) years at an annual interest rate (?). Equation: PMT=P(r/n)/[1-(1+r/n)^-nt ]

The formula provided calculates the regular payment amount for a loan using the following variables:

\[
PMT = \frac{P\left(\frac{r}{n}\right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}
\]

Here's what each variable represents:

- \( PMT \): The regular payment amount.
- \( P \): The loan principal or the total amount of the loan.
- \( r \): The annual interest rate (expressed as a decimal, e.g., 5% = 0.05).
- \( n \): The number of payments per year.
- \( t \): The number of years the loan is repaid over.

Now, filling in the blanks:

1. \( PMT \) is the **regular payment amount** required to repay the loan.
2. \( P \) is the **loan amount** (principal).
3. \( n \) is the **number of payments per year**.
4. \( t \) is the **number of years** over which the loan is repaid.
5. \( r \) is the **annual interest rate** (as a decimal).

Let me know if you'd like to explore any part of this further or if you have questions!

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**Related questions:**
1. How do changes in the interest rate \(r\) affect the payment amount \(PMT\)?
2. What happens to \(PMT\) if the number of years \(t\) is increased while all other factors stay the same?
3. How can the formula be adjusted for interest rates that change over time?
4. How does the number of payments per year \(n\) impact the overall cost of the loan?
5. How can you use this formula to calculate the total interest paid over the life of the loan?

**Tip:** Always convert percentages to decimals in financial formulas. For example, 5% becomes 0.05.

Fill in the blanks. In the formula below (?) is the regular payment amount required to repay a loan of (?) dollars paid (?) times per year over (?) years at an annual interest rate (?). Equation: PMT=P(r/n)/[1-(1+r/n)^-nt ]

Learn how to calculate the regular payment required to repay a loan using the compound interest formula. This problem covers key algebraic concepts, including loan amortization and the impact of interest rates on payments. Suitable for high school students in Grades 10-12.

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