Use the Car Loan Calculator to do the following: (Click HERE for a calculator)

Question

1. The car you would like cost $20,000. Enter $20,000 in the Auto Loan amount field.

2. Use a 7% interest rate for 5 years. Now, try an 11% interest rate for 5 years. What is the difference in payments?

Now, use a Mortgage Calculator to do the following: (Click HERE for a calculator)

3. Find out your monthly payment for a house worth $200,000 at 8% interest for 30 years.

4. Find the total amount of interest being paid over the life of the loan.

How to find Total Amount of Interest Paid: Scroll down a little and click on the button "Show/ Recalculate Amortization Table", scroll down a little more to find "Total Interest", scroll all the way down to the bottom to see the "Total amount of interest" paid.

5. Change the interest rate to 5%. What is the new payment? What is the total interest paid?

6. Change the years to 15 and keep 5%. What are the payment and total interest paid?

7. What is the difference in interest paid from questions 5 and 6? Understanding consumer and business loans is very important. Take a look at the information above. Were you a little shocked when you saw the real cost of a loan--the interest.

In the home mortgage example, the interest paid back over the life of the loan was over 160% of the amount borrowed!!! And, that is only at 8% interest. Take a minute and play with taking out a loan of $200,000 and change the interest rate. Try one higher than 8% and see how the interest paid over the life of the loan changes. As stated before, it can be shocking!

Answer 1

To perform the calculations you've mentioned, I'll guide you through the steps required for each task using typical values based on your prompts. However, since I can't directly access or click on any external calculators, I'll provide the expected calculations for you.

Car Loan Calculations

1. Auto Loan Amount: $20,000

2. Payments at Different Interest Rates:

   • 7% Interest Rate for 5 years: To calculate the monthly payment, you can use the formula for an amortizing loan:

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

     Where:

     • \( M \) = total monthly payment
     • \( P \) = principal loan amount ($20,000)
     • \( r \) = monthly interest rate (annual rate / 12)
     • \( n \) = number of payments (loan term in months)

     At 7% interest:

     • Monthly interest rate \( r = \frac{0.07}{12} \approx 0.005833 \)
     • Number of payments \( n = 5 \times 12 = 60 \)
     • Plugging in the values:

     \[ M = 20000 \times \frac{0.005833(1 + 0.005833)^{60}}{(1 + 0.005833)^{60} - 1} \approx $396.24 \]

   • 11% Interest Rate for 5 years: At 11% interest:

     • Monthly interest rate \( r = \frac{0.11}{12} \approx 0.009167 \)
     • Plugging in the values:

     \[ M = 20000 \times \frac{0.009167(1 + 0.009167)^{60}}{(1 + 0.009167)^{60} - 1} \approx $425.45 \]

   • Difference in Payments: \[ Difference = 425.45 - 396.24 \approx $29.21 \]

Mortgage Calculations

3. Monthly Payment for a House:

   • House Price: $200,000
   • Interest Rate: 8%
   • Loan Term: 30 years (360 months)

   Using the same formula as above:

   • Monthly interest rate \( r = \frac{0.08}{12} \approx 0.006667 \)
   • Plugging in the values:

   \[ M = 200000 \times \frac{0.006667(1 + 0.006667)^{360}}{(1 + 0.006667)^{360} - 1} \approx $1,467.53 \]

4. Total Amount of Interest Paid:

   • Total payment over 30 years: \( M \times n = 1,467.53 \times 360 \approx $528,109.80 \)
   • Total interest paid:

   \[ Total Interest = Total Payment - Principal = 528,109.80 - 200,000 \approx $328,109.80 \]

5. New Payment at 5% Interest Rate:

   • Monthly interest rate \( r = \frac{0.05}{12} \approx 0.004167 \)
   • Plugging in the values:

   \[ M = 200000 \times \frac{0.004167(1 + 0.004167)^{360}}{(1 + 0.004167)^{360} - 1} \approx $1,073.64 \]

   Total Interest Paid:

   • Total payment over 30 years: \( 1,073.64 \times 360 \approx $386,914.40 \)
   • Total interest paid:

   \[ Total Interest = 386,914.40 - 200,000 \approx $186,914.40 \]

6. Payment and Total Interest Paid with 5% for 15 Years:

   • New loan term: 15 years (180 months)
   • Monthly interest rate \( r = \frac{0.05}{12} \approx 0.004167 \)
   • Plugging in the values:

   \[ M = 200000 \times \frac{0.004167(1 + 0.004167)^{180}}{(1 + 0.004167)^{180} - 1} \approx $1,588.53 \]

   Total Interest Paid:

   • Total payment over 15 years: \( 1,588.53 \times 180 \approx $285,936.40 \)
   • Total interest paid:

   \[ Total Interest = 285,936.40 - 200,000 \approx $85,936.40 \]

7. Difference in Interest Paid:

   • From question 5: \( 186,914.40 \)
   • From question 6: \( 85,936.40 \)
   • Difference:

   \[ Difference = 186,914.40 - 85,936.40 = 100,978.00 \]

Summary

• Car Loan Difference: $29.21
• Mortgage Payments:
  • At 8% for 30 years: $1,467.53 total interest: $328,109.80
  • At 5% for 30 years: $1,073.64 total interest: $186,914.40
  • At 5% for 15 years: $1,588.53 total interest: $85,936.40
• Interest Difference (30yrs 5% and 15yrs 5%): $100,978.00

The calculations demonstrate how interest significantly affects the total loan cost over time. High interest rates and long loan durations can lead to substantial amounts paid in interest.