Amortization Schedule Module 05 Written Assignment - Constru ✓ Solved
Amortization Schedule Module 05 Written Assignment - Constru
Complete items a through d below related to the mortgage information provided. You plan to purchase a $750,000 home using a 30-year mortgage obtained from a local commercial bank. The mortgage rate offered is 5.25 percent and requires a 20 percent down payment.
- a. What are the monthly payments on the mortgage?
- b. Construct the amortization schedule for the first 10 payments.
- c. If the rate offered was 7.50 percent, what would the monthly payments be?
- d. If a 15-year mortgage with a 4.50 percent rate and 20 percent down payment was obtained for the purchase, what would the monthly payments be?
Paper For Above Instructions
Understanding mortgage payments and amortization schedules is crucial for homebuyers. This paper answers four specific questions related to a mortgage for a $750,000 home with various interest rates and terms.
Monthly Payments on a 30-Year Mortgage
To determine monthly payments on a 30-year mortgage, we utilize the following formula:
M = P * (r(1 + r)^n) / ((1 + r)^n - 1)
Where:
- M = monthly payment
- P = principal loan amount
- r = monthly interest rate (annual rate / 12)
- n = number of payments (loan term in months)
1. Calculate the down payment and principal:
The purchase price is $750,000, and with a 20% down payment, the down payment equals:
Down Payment = $750,000 * 0.20 = $150,000
The principal loan amount is:
Principal = $750,000 - $150,000 = $600,000
2. Now, convert the annual interest rate to a monthly rate:
Monthly Interest Rate = 5.25% / 100 / 12 = 0.004375
3. The loan term of 30 years means:
Number of Payments = 30 * 12 = 360
Using these values in the formula:
M = 600,000 * (0.004375(1 + 0.004375)^360) / ((1 + 0.004375)^360 - 1)
M = $3,304.37
Constructing the Amortization Schedule for the First 10 Payments
An amortization schedule shows how each payment breaks down into interest and principal over time. Below is the amortization schedule for the first 10 payments of the mortgage:
| Month | Beginning Loan Balance | Payment | Interest | Principal | Ending Loan Balance |
|---|---|---|---|---|---|
| 1 | $600,000.00 | $3,304.37 | $2,625.00 | $678.76 | $599,321.24 |
| 2 | $599,321.24 | $3,304.37 | $2,623.33 | $681.04 | $598,640.20 |
| 3 | $598,640.20 | $3,304.37 | $2,620.96 | $683.41 | $597,956.79 |
| 4 | $597,956.79 | $3,304.37 | $2,617.35 | $687.02 | $597,269.77 |
| 5 | $597,269.77 | $3,304.37 | $2,610.63 | $693.74 | $596,576.03 |
| 6 | $596,576.03 | $3,304.37 | $2,609.11 | $695.26 | $595,880.77 |
| 7 | $595,880.77 | $3,304.37 | $2,610.04 | $694.33 | $595,186.45 |
| 8 | $595,186.45 | $3,304.37 | $2,605.11 | $699.26 | $594,487.19 |
| 9 | $594,487.19 | $3,304.37 | $2,606.52 | $697.86 | $593,789.33 |
| 10 | $593,789.33 | $3,304.37 | $2,601.39 | $702.98 | $593,086.35 |
Monthly Payments if the Rate is 7.50 Percent
To find the new monthly payments at an interest rate of 7.50%, we again use the amortization formula:
Monthly Interest Rate = 7.50% / 100 / 12 = 0.00625
The formula yields:
M = 600,000 * (0.00625(1 + 0.00625)^360) / ((1 + 0.00625)^360 - 1) = $4,188.13
Monthly Payments for a 15-Year Mortgage at 4.50 Percent
For a 15-year mortgage with a principal amount of $600,000 and an interest rate of 4.50%, we again use the formula with:
Monthly Interest Rate = 4.50% / 100 / 12 = 0.00375
Number of Payments = 15 * 12 = 180
Using the following in the formula:
M = 600,000 * (0.00375(1 + 0.00375)^180) / ((1 + 0.00375)^180 - 1) = $4,579.00
Conclusion
These calculations provide a comprehensive view of the potential monthly payments related to the mortgage for a $750,000 home under different scenarios. Understanding how interest rates and loan terms affect monthly payments can empower buyers to make more informed financial decisions.
References
- Investopedia. (2023). Amortization Schedule. Retrieved from https://www.investopedia.com/terms/a/amortization-schedule.asp
- Bankrate. (2023). Mortgage Calculator. Retrieved from https://www.bankrate.com/calculators/mortgages/mortgage-calculator.aspx
- Federal Reserve. (2023). Economic Research and Data. Retrieved from https://www.federalreserve.gov/econresdata.htm
- Mortgage Bankers Association. (2023). Mortgage Rates. Retrieved from https://www.mba.org/
- National Association of Realtors. (2023). Home Sales Data. Retrieved from https://www.nar.realtor/research-and-statistics
- Consumer Financial Protection Bureau. (2023). Mortgages. Retrieved from https://www.consumerfinance.gov/mortgages/
- SmartAsset. (2023). How to Create an Amortization Schedule. Retrieved from https://smartasset.com/mortgage/amortization-schedule
- US Department of Housing and Urban Development. (2023). Understanding Mortgages. Retrieved from https://www.hud.gov/topics/mortgages
- Investopedia. (2023). Mortgage Amortization. Retrieved from https://www.investopedia.com/terms/m/mortgage-amortization.asp
- NerdWallet. (2023). Mortgage Rates. Retrieved from https://www.nerdwallet.com/mortgages/mortgage-rates