After graduating with a master's degree, Lacee combined all of her student loans into a single loan of $15,000.00 with an interest rate of 3.2% compounded quarterly. If she is planning to pay off the loan in 12 years, what will her quarterly payment be?

The quarterly payment would be $. (Round to 2 decimal places.)




To find Lacee's quarterly payment, we can use the formula for the payment on an amortized loan:

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

Where:
- $PMT$ is the quarterly payment,
- $P$ is the principal loan amount,
- $r$ is the interest rate per period (quarterly in this case),
- $n$ is the number of periods per year (quarterly, so 4),
- $t$ is the total number of years.

### Given:
- $P = 15,000$ (loan amount),
- Annual interest rate = 3.2%, compounded quarterly,
- $n = 4$,
- $t = 12$ years.

### Steps:
1. The quarterly interest rate ($r$) is:

\[
r = \frac{3.2\%}{4} = \frac{0.032}{4} = 0.008
\]

2. The total number of periods is:

\[
n \times t = 4 \times 12 = 48
\]

Now, let’s compute the quarterly payment using these values.

The quarterly payment for Lacee's loan will be approximately **$377.56**.

Would you like further details on the calculation or have any additional questions?

Here are five related questions to consider:
1. How does the total interest paid over the life of the loan get calculated?
2. What happens if Lacee pays an additional amount each quarter?
3. How would the quarterly payment change if the interest rate were compounded monthly instead of quarterly?
4. What is the difference between simple interest and compound interest?
5. How does the term (number of years) affect the total amount paid over the life of the loan?

**Tip:** Increasing the frequency of payments (e.g., switching from quarterly to monthly) can reduce the total interest paid over the loan's life.

After graduating with a master's degree, Lacee combined all of her student loans into a single loan of $15,000.00 with an interest rate of 3.2% compounded quarterly. If she is planning to pay off the loan in 12 years, what will her quarterly payment be?

Calculate the quarterly payment for a $15,000 student loan with a 3.2% interest rate compounded quarterly, to be paid off in 12 years. This problem involves the amortized loan payment formula and compound interest concepts, making it ideal for high school and college-level students.

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