Adrian is looking to take out a mortgage for dollar sign, 210, comma, 000$210,000 from a bank offering a monthly interest rate of 0.525%. Using the formula below, determine his monthly payment, to the nearest dollar, if the loan is taken over 30 years.
M, equals, start fraction, P, r, left parenthesis, 1, plus, r, right parenthesis, to the power n , divided by, left parenthesis, 1, plus, r, right parenthesis, to the power n , minus, 1, end fraction
M=
(1+r)
n
−1
Pr(1+r)
n

​

M, equalsM= the monthly payment
P, equalsP= the amount borrowed
r, equalsr= the interest rate per month
n, equalsn= the number of payments

To calculate Adrian's monthly mortgage payment, we can use the formula for a fixed-rate mortgage:

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

Where:
- $ M $ is the monthly payment
- $ P = 210,000 $ (the loan amount)
- $ r = 0.00525 $ (monthly interest rate, since 0.525% = 0.00525 in decimal form)
- $ n = 360 $ (the total number of monthly payments over 30 years, which is $ 30 \times 12 $)

### Step 1: Calculate the terms in the formula
1. $ (1 + r) = 1 + 0.00525 = 1.00525 $
2. Raise $ (1 + r) $ to the power of $ n $:
   \[
   (1.00525)^{360}
   \]
3. Calculate the numerator $ P \cdot r \cdot (1 + r)^n $.
4. Calculate the denominator $ (1 + r)^n - 1 $.

### Step 2: Apply the formula

Let me calculate this for you.Adrian's monthly mortgage payment would be approximately **$1,300**.

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

Here are 5 related questions to deepen your understanding:
1. What happens to the monthly payment if the interest rate increases to 0.6% per month?
2. How does the loan term (30 years) affect the monthly payment compared to a 15-year loan?
3. What is the total amount Adrian would pay over the entire loan period?
4. How much of Adrian's first payment goes towards interest versus principal?
5. How can Adrian reduce the total interest paid over the life of the loan?

**Tip:** Reducing the loan term from 30 years to 15 years can significantly lower the total interest paid, but it will increase monthly payments.

Adrian is looking to take out a mortgage for $210,000 from a bank offering a monthly interest rate of 0.525%. Using the formula below, determine his monthly payment, to the nearest dollar, if the loan is taken over 30 years.

Learn how to calculate the monthly mortgage payment for a $210,000 loan with a 0.525% monthly interest rate over 30 years using a standard fixed-rate mortgage formula. This solution covers algebraic and financial concepts, ideal for students in Grades 10-12.

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