Applied Math - Finances - Refinancing Loans

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Introduction

Home loans are typically 30 years in length. A lot can change in that time. If a family has an 8% interest rate on a home loan, then 15 years later the interest rate drops to 3%, they might want to "refinance" the loan. Refinancing the loan is usually a process where the lender gets a new loan. Bank A might have given them their original loan, but bank B might be the ones financing their new loan at a lower rate (or the same bank could offer a new rate).

Refinancing a loan costs some money up front. It also takes time to attend the required meetings. When is it worth it for a family to refinance a loan?

Credit cards, student loans, auto loans, etc. can also be refinanced.

Example:

1.

A family is currently paying a loan for their $240,000 house. The interest rate is 8%. The monthly payments are $1,761. They have 15 more years left on the loan. They still owe $184,275.74 out of the original $240,000 loan.

They explore refinancing options and determine that a 15 year refinance at 4% is their best option. They will make monthly payments of $1,363 if they refinance.

All of these items have to be paid if they decide to refinance.

Should the family refinance?

If they stick with their original loan, their total cost for the final 15 years will be

\(\$1,761 \text{ per month }\cdot 12 \text{ months} \cdot 15 \text{ years} =\)

\(\$316,980\)

If they refinance, their monthly payments will cost

\(\$1,363 \text{ per month }\cdot 12 \text{ months} \cdot 15 \text{ years} =\)

\(\$245,340\)

We have to add in the cost of refinancing, though.

The application fee is \(\$184,275.74 \cdot 0.015 = \$2,764.14\)

The appraisal is $500

The title search is $200

The title insurance is $1,000

The closing costs are \(\$184,275.74 \cdot 0.03 = \$5,528.27\)

The total cost of paying back the loan with refinancing is

\(\$245,340 + \$2,764.14 + \$500 + \$200 + \$1,000 + \$5,528.27 =\)

\(\$255,332.41\)

They will save a lot of money if they refinance the loan, even with the fees in mind.



2. A family has $4,000 of credit card debt for one credit card at 20% interest. If they only make minimum payments, they will have to pay $200 a month for 2 years and one month to pay off the credit card.

The family also has $6,000 in credit card debt at 25% interest. The family can afford to pay $250 a month on this card. The payments will last 2 years and 10 months at this rate.

The family also has student loan debt of $20,000. The debt has an average interest rate of 6%. They are on a 15 year payment plan for $169 a month.

The family could take out a personal loan to pay off the debt. They have the option to take out a personal loan for 5 years for $10,000 at 9% interest. Their monthly payment would be $207.58. The family could also take out a personal loan for $30,000 at 9% interest for 7 years. Their monthly payment would be $482.67.

How should the family refinance their debt to save interest in the long run?

The family should avoid taking out the personal loan to cover the cost of student loans if they can afford the monthly payments. The student loans have a lower interest rate than the personal loans.

If the family finances just the credit card debt of $10,000, they will save money as the interest rate is much lower.

If they stuck to the payment plan of the credit cards, their total cost would be

\[\$200 \text{ per month} \cdot 25 \text{ months} = \$5,000\]

\[\$250 \text{ per month} \cdot 34 \text{ months} = \$8,500\]

If they refinance the credit cards using the $10,000 refinancing option at 9% interest, their total cost would be

\[\$207.58 \text{ per month} \cdot 12 \text{ months} \cdot 5 \text{ years} = \$12,454.80\]

The personal loan saves the family \((\$5,000 + \$8,500) - \$12,454.80 = \$1,045.20\) in the long run. Also, the personal loan has a lower monthly payment of $207.58, compared to the larger combined monthly payments of $200 and $250

Practice Problems

1. A family is currently paying a loan for their $240,000 house. The interest rate is 8%. The monthly payments are $1,761. They have 15 more years left on the loan. They still owe $184,275.74 out of the original $240,000 loan.

They explore refinancing options and determine that a 15 year refinance at 4% is their best option. They will make monthly payments of $1,363 if they refinance.

All of these items have to be paid if they decide to refinance.

Should the family refinance?



2.

A family has $4,000 of credit card debt for one credit card at 20% interest. If they only make minimum payments, they will have to pay $200 a month for 2 years and one month to pay off the credit card.

The family also has $6,000 in credit card debt at 25% interest. The family can afford to pay $250 a month on this card. The payments will last 2 years and 10 months at this rate.

The family also has student loan debt of $20,000. The debt has an average interest rate of 6%. They are on a 15 year payment plan for $169 a month.

The family could take out a personal loan to pay off the debt. They have the option to take out a personal loan for 5 years for $10,000 at 9% interest. Their monthly payment would be $207.58. The family could also take out a personal loan for $30,000 at 9% interest for 7 years. Their monthly payment would be $482.67.

How should the family refinance their debt to save interest in the long run?

Theory Questions