To calculate the monthly mortgage payment $P$, we can use the mortgage formula:

$P = \frac{r \cdot PV}{1 - (1 + r)^{-n}}$

Where:

• $P$ is the monthly payment (in kUSD),
• $r$ is the monthly interest rate,
• $PV$ is the loan principal (the amount of the mortgage in kUSD),
• $n$ is the total number of monthly payments.

Let's break this down step by step:

Step 1: Calculate the loan principal $PV$

The couple put down 20% on the house, meaning they financed the remaining 80% with a mortgage.

$PV = 80\% \times 500 = 0.80 \times 500 = 400 \text{ kUSD}$

Step 2: Determine the interest rate and number of payments

• The annual interest rate is 10%, so the monthly interest rate is:

$r = \frac{10\%}{12} = \frac{0.10}{12} = 0.0083333$

• The mortgage is for 15 years, and since payments are made monthly, the total number of payments $n$ is:

$n = 15 \times 12 = 180 \text{ months}$

Step 3: Use the mortgage formula to calculate $P$

Now that we have all the necessary values, we can plug them into the mortgage formula:

$P = \frac{0.0083333 \times 400}{1 - (1 + 0.0083333)^{-180}}$

Let me compute that value for $P$.The monthly mortgage payment $P$ is approximately 4.30 kUSD.

Would you like more details or have any questions? Here are some related questions to explore:

1. How much total interest will the couple pay over the life of the loan?
2. What is the remaining loan balance after 8 years of payments?
3. How much equity has the couple built up after 8 years?
4. What would be the impact of an extra monthly payment on the loan?
5. How does the market value increase affect their total financial position?

Tip: Making extra payments on a mortgage can significantly reduce the total interest paid over the loan term.