An executive wishes to take out a
$
1,200,000
mortgage. The yearly interest rate on the loan is
1.95
%
and the loan is for
20
years. Payments will be made monthly. Calculate the monthly payment to the nearest cent. Do not include the dollar symbol or commas.

Provide your answer below:

We can calculate the monthly payment for the mortgage using the formula for the monthly payment of a fixed-rate loan:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount (\$1,200,000).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of payments (loan term in years multiplied by 12).

### Step-by-step solution:
1. **Loan amount (P)** = 1,200,000
2. **Annual interest rate** = 1.95% = 0.0195
3. **Monthly interest rate (r)** = $ \frac{0.0195}{12} = 0.001625 $
4. **Total number of payments (n)** = $ 20 \times 12 = 240 $

Now, plug these values into the formula:

\[
M = 1,200,000 \times \frac{0.001625(1 + 0.001625)^{240}}{(1 + 0.001625)^{240} - 1}
\]

I'll calculate this next.The monthly payment for the mortgage is approximately $ 6042.23 $ (to the nearest cent).

Do you have any questions or would you like more details?

Here are 5 related questions to expand on this:

1. How does increasing the loan term affect the monthly payments?
2. What would the monthly payment be if the interest rate increased to 3%?
3. How much total interest will be paid over the life of the loan?
4. How does a larger down payment affect the monthly payment?
5. What would be the monthly payment if the loan amount were increased to $1,500,000?

**Tip:** When calculating monthly payments for loans, always check if the interest rate is compounded monthly to use the correct formula!

An executive wishes to take out a $1,200,000 mortgage. The yearly interest rate on the loan is 1.95% and the loan is for 20 years. Payments will be made monthly. Calculate the monthly payment to the nearest cent. Do not include the dollar symbol or commas.

Calculate the monthly mortgage payment for a $1,200,000 loan with a 1.95% interest rate over 20 years. Step-by-step guide with key formulas and concepts in loan amortization. Ideal for students and professionals interested in financial mathematics.

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