To determine how much Sarah will still owe on her house in 5 years, we need to calculate the remaining balance on the mortgage. This can be done using the amortization formula.

The formula for the remaining balance $B(t)$ after $t$ months on an amortized loan is:

$B(t) = P \cdot \frac{(1 + r)^N - (1 + r)^t}{(1 + r)^N - 1}$

Where:

• $P$ is the principal (loan amount),
• $r$ is the monthly interest rate,
• $N$ is the total number of payments (loan term in months),
• $t$ is the number of payments already made.

Step 1: Define the values

• Principal $P = 190,000$ dollars,
• Annual interest rate = 3% or 0.03,
• Monthly interest rate $r = \frac{0.03}{12} = 0.0025$,
• Term $N = 15 \times 12 = 180$ months,
• Time after 5 years $t = 5 \times 12 = 60$ months.

Step 2: Apply these values into the formula

Now, I will calculate the remaining balance using the amortization formula.After 5 years, Sarah will still owe approximately $135,883.91 on her house.

Would you like further details on how this calculation was made, or do you have any questions?

Here are 5 related questions to explore:

1. How can Sarah reduce the amount owed after 5 years?
2. What would her monthly payment be over the 15-year term?
3. How does the amortization schedule break down between interest and principal over time?
4. What would the remaining balance be if the interest rate were 4% instead of 3%?
5. How would early payments or extra payments affect her remaining balance?

Tip: Making extra payments directly toward the principal can significantly reduce the total interest paid over the loan term.