If they choose a 30-year fixed mortgage loan, they will have an interest rate is 7.216%. What would their monthly payment have to be to pay off the loan in 30 years? 2. If they choose a 20-year fixed mortgage loan, they will have an interest rate of 7.042%. What would their monthly payment have to be to pay off the loan in 20 years? 3. If they choose a 15-year fixed mortgage loan, they will have an interest rate of 6.181%. What would their monthly payment have to be to pay off the loan in 15 years? 4. Bizzie and Jay chose the loan with the lowest monthly payment. a. How much total interest will be paid on the loan by the end of the payment period? b. If Bizzie and Jay decide to add $300 to their required mortgage payment every month, how long will it take to pay off their loan? c. After making payments for 10 years, they decided to refinance their loan. i. What is the remaining balance on their loan? ii. How much has been paid in interest by the end of the 10 years?

To calculate the monthly mortgage payments, total interest, and other related values, we need to use the mortgage payment formula, which is given by:

\[
M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]

Where:
- $M$ is the monthly payment.
- $P$ is the principal loan amount.
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the number of payments (loan term in years multiplied by 12).

Let’s go through each part of your query step-by-step:

### 1. Monthly payment for a 30-year fixed mortgage at 7.216%
\[
r = \frac{7.216\%}{12} = 0.0060133
\]
\[
n = 30 \times 12 = 360 \text{ months}
\]

Using the mortgage formula, we can determine the monthly payment $M$, but the principal loan amount $P$ is not specified. Could you provide that information?

### 2. Monthly payment for a 20-year fixed mortgage at 7.042%
\[
r = \frac{7.042\%}{12} = 0.0058683
\]
\[
n = 20 \times 12 = 240 \text{ months}
\]

Similarly, we need the loan amount $P$ to calculate the exact payment.

### 3. Monthly payment for a 15-year fixed mortgage at 6.181%
\[
r = \frac{6.181\%}{12} = 0.0051508
\]
\[
n = 15 \times 12 = 180 \text{ months}
\]

Again, the loan amount $P$ is needed to determine the payment.

### 4. Bizzie and Jay chose the loan with the lowest monthly payment.

- **a. Total interest paid on the loan by the end of the payment period:**
  
  Total interest paid can be calculated by:
  \[
  \text{Total interest} = (\text{Monthly payment} \times \text{Number of payments}) - \text{Loan amount}
  \]

- **b. If they add $300 to their monthly payment, how long will it take to pay off the loan?**
  
  We can calculate the new loan term by adjusting the monthly payment and solving for the new number of months needed to pay off the loan.

- **c. After 10 years of payments, if they refinance the loan:**
  
  - **i. Remaining balance on the loan:** We use the amortization formula to determine the remaining balance after 10 years.
  - **ii. Total interest paid in the first 10 years:** This requires summing up all the interest paid in the first 120 payments (10 years).

### Next Steps
To provide exact values, could you clarify the **principal loan amount** $P$ that Bizzie and Jay are considering for these mortgage options? Once we have that, we can compute all the required details.

---

Would you like to see more detailed explanations for any part of the calculation?

Here are five related questions you might find useful:

1. What is the effect of changing the interest rate on a mortgage loan?
2. How can paying extra on a mortgage affect the loan's term?
3. What are the benefits and drawbacks of refinancing a mortgage after 10 years?
4. How can one calculate the remaining balance on a loan after a certain period?
5. How does a shorter loan term compare to a longer one in terms of total interest?

**Tip:** Making extra payments on your mortgage can significantly reduce the total interest paid over the loan's life and shorten the repayment period.

If they choose a 30-year fixed mortgage loan, they will have an interest rate of 7.216%. What would their monthly payment have to be to pay off the loan in 30 years? 2. If they choose a 20-year fixed mortgage loan, they will have an interest rate of 7.042%. What would their monthly payment have to be to pay off the loan in 20 years? 3. If they choose a 15-year fixed mortgage loan, they will have an interest rate of 6.181%. What would their monthly payment have to be to pay off the loan in 15 years? 4. Bizzie and Jay chose the loan with the lowest monthly payment. a. How much total interest will be paid on the loan by the end of the payment period? b. If Bizzie and Jay decide to add $300 to their required mortgage payment every month, how long will it take to pay off their loan? c. After making payments for 10 years, they decided to refinance their loan. i. What is the remaining balance on their loan? ii. How much has been paid in interest by the end of the 10 years?

Learn how to calculate monthly mortgage payments and total interest for different fixed-rate loans: 30-year at 7.216%, 20-year at 7.042%, and 15-year at 6.181%. This problem covers key financial concepts such as amortization and interest calculation. Suitable for college-level or advanced high school students.

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