To calculate the total interest Moira will pay during the 20-year amortization period, we will follow these steps:

Step 1: Calculate the mortgage amount

The total cost of the home is $230,000, and Moira makes a down payment of $25,500.

The mortgage amount is the balance of the purchase price: $\text{Mortgage amount} = 230,000 - 25,500 = 204,500$

Step 2: Apply the mortgage formula for fixed-rate loans

The monthly mortgage payment can be calculated using the formula for a fixed-rate mortgage: $M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$ Where:

• $M$ is the monthly mortgage payment
• $P$ is the loan principal (the mortgage amount), which is $204,500
• $r$ is the monthly interest rate (annual rate divided by 12), which is $\frac{5.25\%}{12} = 0.0525 / 12 = 0.004375$
• $n$ is the total number of payments (the amortization period in months), which is $20 \times 12 = 240$ months

Now, substituting the values into the formula: $M = 204,500 \times \frac{0.004375(1+0.004375)^{240}}{(1+0.004375)^{240} - 1}$

Step 3: Calculate the monthly mortgage payment

Let’s compute this step-by-step:

1. Compute $(1 + r)^{240} = (1 + 0.004375)^{240}$
2. Multiply by $r$
3. Plug values into the full mortgage formula

Now, let's calculate this.

Given values P = 204500 # Mortgage principal amount annual_rate = 5.25 / 100 # Annual interest rate monthly_rate = annual_rate / 12 # Monthly interest rate n = 20 * 12 # Total number of payments (20 years)

Mortgage payment formula

numerator = monthly_rate * (1 + monthly_rate) ** n denominator = (1 + monthly_rate) ** n - 1 monthly_payment = P * numerator / denominator

Total payment over 20 years

total_payment = monthly_payment * n

Total interest paid

total_interest = total_payment - P monthly_payment, total_interestThe monthly mortgage payment Moira will make is approximately $1,378.01.

The total interest Moira will pay over the 20-year amortization period is approximately $126,222.72.

Would you like more details on how this is calculated, or do you have any other questions?

Here are some related questions for further exploration:

1. How does the interest paid change if Moira were to choose a mortgage with a different interest rate (e.g., 4.5% or 6%)?
2. What happens if Moira makes extra payments on her mortgage? How does this affect the total interest paid?
3. How can the mortgage payment formula be derived from the general formula for the sum of a geometric series?
4. How would the total interest paid be affected if Moira had a shorter amortization period, such as 15 years instead of 20 years?
5. What other factors might influence the total interest paid on a mortgage?

Tip: Even small increases in your down payment can lead to significant savings on interest over time, since the mortgage principal would be lower.