uppose you want to borrow

​$110 comma 000110,000

and you find a bank offering a

2020​-year

term for a loan of that​ amount, with an APR of

1212​%.

Complete parts ​(a) and ​(b) below.

Question content area bottom

Part 1

​(a) What are your monthly​ payments?

PMTequals=​$1,211.191,211.19

​(Round to the nearest cent as​ needed.)

Part 2

​(b) Instead of making

1212

payments per​ year, you save enough money to make a

1313th

payment each​ year, of the same amount as your regular monthly payment found in part

​(a).

How long will it take to pay off the​ loan?

Yequals=2020

​(Type an integer or decimal rounded to one decimal place as​ needed.)

Let's break down the problem:

### Part 1 (already given):
- **Loan amount (PV):** \$110,000
- **Term:** 20 years
- **Annual Percentage Rate (APR):** 12% (nominal annual rate)
- **Monthly payments (PMT):** \$1,211.19 (calculated using the standard loan formula).

The monthly payment was already provided as \$1,211.19, so let's focus on part 2.

### Part 2:
Instead of making 12 monthly payments per year, you plan to make a 13th payment each year, which will reduce the total loan term. We need to calculate how long it will take to pay off the loan with these extra payments.

---

### Step-by-step approach for part (b):

1. **Annual nominal interest rate (APR):** 12%
2. **Monthly interest rate:** $ \frac{12\%}{12} = 1\% $
3. **Monthly payment (PMT):** \$1,211.19
4. **Additional annual payment:** Since you make one additional payment each year, your effective annual number of payments is $ 12 + 1 = 13 $.
5. **Loan term with extra payment:** The loan balance decreases faster with the extra payment, so we need to recalculate how long it will take to pay off the loan.

We'll use the formula for the number of payments required for loan repayment with extra payments.

I'll calculate the new loan term based on the extra payment of \$1,211.19 per year.With the extra 13th payment each year, it will take approximately **15.3 years** to pay off the loan, instead of the original 20 years.

Would you like further details or have any questions? 

Here are some related questions for you to consider:
1. How is the loan amortization schedule affected by extra payments?
2. What impact does increasing the APR have on the loan term?
3. How would making two extra payments per year change the loan term?
4. What happens if the extra payment amount is less than or greater than the monthly payment?
5. How can refinancing at a lower interest rate affect the loan term?

**Tip:** Making even small extra payments toward your loan principal can significantly reduce the total interest paid and shorten the loan term.

Suppose you want to borrow $110,000 and you find a bank offering a 20-year term for a loan of that amount, with an APR of 12%. What are your monthly payments? (PMT = $1,211.19) Additionally, if you make a 13th payment each year, how long will it take to pay off the loan?

Learn how to calculate loan payments and the impact of extra payments on a $110,000 loan with a 12% APR over 20 years. This problem covers loan amortization, interest rates, and strategies to reduce loan terms using extra payments. Suitable for Grades 10-12 and finance students.

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