To calculate Brad's monthly mortgage payment, we use the loan amortization formula:

$M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}$

Where:

• $M$ is the monthly payment.
• $P$ is the loan amount (principal) = $210,000.
• $r$ is the monthly interest rate (annual interest rate divided by 12).
• $n$ is the total number of payments (loan term in months).

Step 1: Calculate the values

• $P = 210,000$
• APR ($3.3\%$) → $r = \frac{3.3}{100} \div 12 = 0.00275$
• Loan term: $25 \times 12 = 300$ months

Step 2: Plug values into the formula

$M = 210,000 \cdot \frac{0.00275(1 + 0.00275)^{300}}{(1 + 0.00275)^{300} - 1}$

Break it down:

1. $1 + r = 1 + 0.00275 = 1.00275$
2. $(1.00275)^{300}$: Use a calculator or software to find this value: $(1.00275)^{300} \approx 2.31044$
3. Numerator: $0.00275 \cdot 2.31044 \approx 0.00635471$
4. Denominator: $2.31044 - 1 = 1.31044$
5. Fraction: $\frac{0.00635471}{1.31044} \approx 0.0048502$
6. Multiply by $P = 210,000$: $M = 210,000 \cdot 0.0048502 \approx 1,018.54$

Final Answer:

Brad’s monthly payment is $1,018.54.

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Do you want further breakdowns or explanations? Here are related questions:

1. What happens if Brad chooses a shorter loan term?
2. How much interest will Brad pay over the life of the loan?
3. What is the effect of a 1% increase in the APR?
4. How does rounding affect monthly payment calculations?
5. How much of the payment goes to principal and interest in the first month?

Tip: Always compare loan terms and APRs before committing to a mortgage to minimize lifetime costs.