A couple bought their house 8 years ago for 500 kUSD and put down 20% on the house. On the balance, they took out a 15-year mortgage at 10% per annum with monthly compounding. To payoff the mortage, the couple paid a constant amount P (kUSD) every month. Suppose that the current net market value is now 800 kUSD and the couple wants to sell their house. Note that the first monthly payment is exactly due at one month after the loan principal is disbursed.

a. Calculate P in kUSD. (please round all answers to 2 decimal places)

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.

A couple bought their house 8 years ago for 500 kUSD and put down 20% on the house. On the balance, they took out a 15-year mortgage at 10% per annum with monthly compounding. To payoff the mortgage, the couple paid a constant amount P (kUSD) every month. Suppose that the current net market value is now 800 kUSD and the couple wants to sell their house. Note that the first monthly payment is exactly due at one month after the loan principal is disbursed.

 a. Calculate P in kUSD. (please round all answers to 2 decimal places)

Learn how to calculate the monthly mortgage payment (P) for a 15-year loan with a 10% interest rate, based on a house purchase price of 500 kUSD with 20% down. Understand key finance concepts such as loan amortization, time value of money, and monthly compounding.

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