To determine the quarterly mortgage payment, we can use the formula for the monthly payment of a loan with compound interest, specifically the amortization formula. The formula for the quarterly payment $P$ on a loan is:

$P = \frac{P_0 \cdot \left( \frac{r}{n} \right)}{1 - \left( 1 + \frac{r}{n} \right)^{-nt}}$

Where:

• $P_0$ is the principal amount (the loan amount), which is $240,000.
• $r$ is the annual interest rate (as a decimal), so $r = 0.066$ for 6.6%.
• $n$ is the number of compounding periods per year (quarterly, so $n = 4$).
• $t$ is the loan term in years (15 years).

Now, plug in the values into the formula:

$P = \frac{240,000 \cdot \left( \frac{0.066}{4} \right)}{1 - \left( 1 + \frac{0.066}{4} \right)^{-4 \cdot 15}}$

Step 1: Simplify the components

• $\frac{0.066}{4} = 0.0165$
• $n \cdot t = 4 \times 15 = 60$

Thus, the formula becomes:

$P = \frac{240,000 \cdot 0.0165}{1 - (1 + 0.0165)^{-60}}$

Step 2: Calculate the denominator

First, calculate $(1 + 0.0165)^{-60}$:

$1 + 0.0165 = 1.0165$

Now raise it to the power of $-60$:

$1.0165^{-60} \approx 0.3774$

Now compute the full denominator:

$1 - 0.3774 = 0.6226$

Step 3: Calculate the final payment

Now compute the full formula:

$P = \frac{240,000 \cdot 0.0165}{0.6226} \approx \frac{3,960}{0.6226} \approx 6,354.56$

So, the quarterly payment is approximately $6,354.56.

Final Answer:

The Taylors' quarterly mortgage payment will be approximately $6,354.56.

Would you like further details on how this was calculated? Or do you have any other questions?

Here are some related questions:

1. How can you adjust the payment formula for monthly payments instead of quarterly?
2. What would happen if the interest rate increased to 8%?
3. How do changes in the loan term (e.g., 10 years) affect the quarterly payment?
4. What is the total amount paid over the life of the loan?
5. How does compound interest affect the total amount paid over time?

Tip: Always check if the interest is compounded on a different frequency (like monthly or annually), as this changes the value of $n$ in the formula.