Question: Task 4: Thinking
11. Research the cost of a home of your choice in your area. Research the current interest rate for a five-year fixed-rate mortgage.
a. What is the price of the home you have chosen?
b. What is the current interest rate for a five-year fixed-rate mortgage?
c. Determine the monthly payment with an amortization period of 25 years.
d. Calculate the total principal paid on the mortgage over the 5-year term.
e. Calculate the total interest paid over five years.
1. **State the problem:**
We want to calculate the monthly mortgage payment, total principal paid, and total interest paid over a 5-year term for a home loan.
2. **Given:**
- Home price: $P$ (you must input the actual price)
- Interest rate (annual, fixed for 5 years): $r$ (as a decimal, e.g., 0.05 for 5%)
- Amortization period: 25 years
- Term length: 5 years
3. **Formula for monthly mortgage payment:**
$$ M = P \times \frac{\frac{r}{12}}{1 - (1 + \frac{r}{12})^{-12 \times 25}} $$
where $M$ is the monthly payment, $P$ is the principal (loan amount), and $r$ is the annual interest rate.
4. **Calculate monthly payment $M$:**
Substitute your values for $P$ and $r$ into the formula.
5. **Calculate total payments over 5 years:**
$$ \text{Total payments} = M \times 12 \times 5 $$
6. **Calculate remaining balance after 5 years:**
Use the formula for remaining balance after $n$ payments:
$$ B = P \times (1 + \frac{r}{12})^{12 \times 5} - M \times \frac{(1 + \frac{r}{12})^{12 \times 5} - 1}{\frac{r}{12}} $$
7. **Calculate total principal paid over 5 years:**
$$ \text{Principal paid} = P - B $$
8. **Calculate total interest paid over 5 years:**
$$ \text{Interest paid} = \text{Total payments} - \text{Principal paid} $$
**Note:** You need to input the actual home price and interest rate to compute numeric answers.
This method helps you understand how much you pay monthly, how much principal you reduce, and how much interest you pay in the first 5 years of a 25-year mortgage.