Find the periodic payment R required to amortize a loan of P dollars over t years with interest charged at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)
P = 60,000, r = 5.5, t = 18, m = 4
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Incorrect: Your answer is incorrect.

Which formula should you use to calculate the periodic payment R to amortize the given loan?

To calculate the periodic payment $ R $ required to amortize a loan, you should use the **amortization formula**:

\[
R = \frac{P \cdot i}{1 - (1 + i)^{-n}}
\]

Where:
- $ P $ is the loan amount (principal),
- $ i $ is the interest rate per period, which is calculated as $ \frac{r}{m} $,
- $ r $ is the annual interest rate as a decimal (so 5.5% = 0.055),
- $ m $ is the number of compounding periods per year,
- $ n $ is the total number of payments, calculated as $ m \cdot t $ where $ t $ is the number of years.

### Step-by-step approach for your given values:
- $ P = 60,000 $
- $ r = 5.5\% = 0.055 $
- $ t = 18 $ years
- $ m = 4 $ (quarterly payments)

### 1. Calculate the interest rate per period $ i $:
\[
i = \frac{r}{m} = \frac{0.055}{4} = 0.01375
\]

### 2. Calculate the total number of payments $ n $:
\[
n = m \cdot t = 4 \cdot 18 = 72
\]

### 3. Substitute into the amortization formula:
\[
R = \frac{60,000 \cdot 0.01375}{1 - (1 + 0.01375)^{-72}}
\]

### 4. Compute the value:
You can use a calculator for this, but first calculate the denominator part:
\[
(1 + 0.01375)^{-72} = 0.3766 \quad \text{(approx.)}
\]
So, the formula becomes:
\[
R = \frac{60,000 \cdot 0.01375}{1 - 0.3766} = \frac{825}{0.6234} \approx 1323.24
\]

Thus, the required periodic payment $ R $ is approximately **$1,323.24**.

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Would you like a detailed explanation of any specific step or a breakdown of the computations?

### Related Questions:
1. How does increasing the number of compounding periods affect the periodic payment?
2. What happens to the loan payment if the interest rate is reduced?
3. How can you calculate the total amount paid over the life of the loan?
4. What is the impact of making additional payments toward the principal?
5. How do you compute the remaining balance after a certain number of payments?

### Tip:
Always double-check the total number of periods when calculating the loan amortization—this can significantly affect your payment calculation.

Find the periodic payment R required to amortize a loan of P dollars over t years with interest charged at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.) P = 60,000, r = 5.5, t = 18, m = 4

Discover how to calculate the periodic payment required to amortize a $60,000 loan over 18 years with a 5.5% interest rate, compounded quarterly. The step-by-step solution uses the amortization formula to provide a detailed breakdown. Perfect for advanced high school or college-level students.

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