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Question about loan amortization

Loan Amortization
When Evelyn and Paul Peters were "house hunting" five years ago, the mortgage rates were pretty high. The fixed rate on a 30-year mortgage was 8.75% while the 15-year fixed rate was at 8%. After walking through many homes, they finally reached a consensus and decided to buy a $200,000 twostory house in an up and coming suburban neighborhood in the Midwest. To avoid prepaid mortgage insurance (PMI) the couple had to borrow from family members and come up with the 20% down payment and the additional required closing costs. Since Evelyn and Paul had already accumulated
significant credit card debt and were still paying off their college loans, they decided to opt for lower monthly payments by taking on a 30-year mortgage, despite its higher interest rate.

Currently, due to a worsening of economic conditions, mortgage rates have come down
significantly and the "refinancing" frenzy is under way. Evelyn and Paul have seen 15-year fixed rates (with no closing costs) advertised at 5% and 30-year rates at 5.75%. Evelyn and Paul realize that refinancing is quite a hassle due to all the paperwork involved but with rates being down to 30-year lows, they don't want to let this opportunity pass them by. About 2 years ago, rates were down to similar levels but they had procrastinated, and had missed the boat. This time, however, the couple called their mortgage officer at the Uptown Bank and locked in the 5%, 15-year rate. Nothing was going to stop them from reducing the costs of paying off their dream house this time!

Questions:
1. What is Evelyn and Paul's monthly mortgage payment prior to the refinancing?
2. During the first 5 years of owing their dream home, how much money has the couple paid towards the mortgage? What proportion of this has been applied toward interest?
3. Had the couple opted for the original 15-year mortgage proposal (15 year, 8%), how much higher would their monthly payment have been?
4. Under the original 15-year, 8% mortgage option, how much total interest would have been paid over the life of the loan? How does this compare with the total interest that would be paid on the 30-year, 8.75% mortgage?
5. If the Peters had chosen the original 15-year, 8% mortgage proposal, how much tax shelter would they have lost (over the last five years) as compared to the 30-year, 8.75% mortgage? Assume the Peter's tax rate is 30%.
6. If the house is currently worth $245,000 and most lenders are willing to lend up to 90% of home value, how much excess equity can the Peters cash out?
7. Should Evelyn and Paul cash out the excess equity that they have built up? Assume money market rates are 4%.
8. Should Evelyn and Paul go ahead and close the 5%, 15 year mortgage? Explain your answer with suitable calculations.

Solution Preview

Loan Amortization
When Evelyn and Paul Peters were "house hunting" five years ago, the mortgage rates were pretty high. The fixed rate on a 30-year mortgage was 8.75% while the 15-year fixed rate was at 8%. After walking through many homes, they finally reached a consensus and decided to buy a $200,000 twostory house in an up and coming suburban neighborhood in the Midwest. To avoid prepaid mortgage insurance (PMI) the couple had to borrow from family members and come up with the 20% down payment and the additional required closing costs. Since Evelyn and Paul had already accumulated
significant credit card debt and were still paying off their college loans, they decided to opt for lower monthly payments by taking on a 30-year mortgage, despite its higher interest rate.

Currently, due to a worsening of economic conditions, mortgage rates have come down
significantly and the "refinancing" frenzy is under way. Evelyn and Paul have seen 15-year fixed rates (with no closing costs) advertised at 5% and 30-year rates at 5.75%. Evelyn and Paul realize that refinancing is quite a hassle due to all the paperwork involved ...

Solution Summary

This solution is comprised of a detailed explanation to answer the following questions: -
1. What is Evelyn and Paul's monthly mortgage payment prior to the refinancing?
2. During the first 5 years of owing their dream home, how much money has the couple paid towards the mortgage? What proportion of this has been applied toward interest?
3. Had the couple opted for the original 15-year mortgage proposal (15 year, 8%), how much higher would their monthly payment have been?
4. Under the original 15-year, 8% mortgage option, how much total interest would have been paid over the life of the loan? How does this compare with the total interest that would be paid on the 30-year, 8.75% mortgage?
5. If the Peters had chosen the original 15-year, 8% mortgage proposal, how much tax shelter would they have lost (over the last five years) as compared to the 30-year, 8.75% mortgage? Assume the Peter's tax rate is 30%.
6. If the house is currently worth $245,000 and most lenders are willing to lend up to 90% of home value, how much excess equity can the Peters cash out?
7. Should Evelyn and Paul cash out the excess equity that they have built up? Assume money market rates are 4%.
8. Should Evelyn and Paul go ahead and close the 5%, 15 year mortgage? Explain your answer with suitable calculations.

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