Five years ago, you bought a house for $151,000. You had a down payment of $30,000, which meant you took out a loan for $121,000. Your interest rate was $5.75% fixed. You would like to pay more on your loan. You check your bank statement and find the following information.
Escrow payment: $211.13
Principle and Interest payment: $706.12
Total payment: $917.25
Current Loan balance: $112,247.47
Then, answer these questions:
1.How much additional money would be needed to add to the monthly payment to pay off the loan in 20 years instead of 25? If you currently meet the monthly expenses with less than $100 left over, would it be reasonable to do this?
2. It might be possible to pay the current balance off in 20 years if you refinanced the loan at a lower interest rate. The interest rate that you qualify for will depend in part on your credit rating. What is the highest interest rate you could refinance at in order to do this. Determine the interest rate that would require a monthly total payment that is less than your current total payment. Also, refinancing costs you a couple of thousand dollars up front in closing costs.
To answer these questions, we need to calculate the monthly payment for the loan if it were to be paid off in 20 years instead of 25.
Step 1: Calculate the new loan term:
New Loan Term = 20 years
Step 2: Convert the interest rate to decimal form:
Interest Rate = 5.75% = 0.0575
Step 3: Calculate the monthly interest rate:
Monthly Interest Rate = Annual Interest Rate / 12 = 0.0575 / 12 = 0.00479
Step 4: Calculate the number of months for the new loan term:
Number of Payments = New Loan Term * 12 = 20 * 12 = 240 months
Step 5: Use the loan balance and the number of payments to calculate the new monthly payment using the formula for a fixed-rate mortgage payment:
Monthly Payment = Loan Balance * (Monthly Interest Rate * (1 + Monthly Interest Rate) ^ Number of Payments) / ((1 + Monthly Interest Rate) ^ Number of Payments - 1)
Substituting the values:
Monthly Payment = $112,247.47 * (0.00479 * (1 + 0.00479) ^ 240) / ((1 + 0.00479) ^ 240 - 1)
Calculating this will give us the new monthly payment.
Now, we can answer your questions:
1. To calculate the additional money needed to add to the monthly payment to pay off the loan in 20 years instead of 25, we need to find the difference between the new monthly payment and the current principle and interest payment.
Additional Monthly Payment = New Monthly Payment - Current Monthly Payment
2. To determine the highest interest rate you could refinance at in order to pay off the current balance in 20 years while having a monthly total payment that is less than your current total payment, we need to find the new monthly payment with the refinanced loan. We can then use this to calculate the maximum interest rate.
Refinanced Monthly Payment = (Current Loan Balance + Closing Costs) * (Monthly Interest Rate * (1 + Monthly Interest Rate) ^ Number of Payments) / ((1 + Monthly Interest Rate) ^ Number of Payments - 1)
Once we have the refinanced monthly payment, we can calculate the highest interest rate using the formula:
Max Interest Rate = (Refinanced Monthly Payment / Current Total Payment - 1) * 12
Remember to add the closing costs to the current loan balance when calculating the refinanced monthly payment.
Now let's perform the calculations step by step to find the answers.
To answer question 1, we need to calculate the additional money needed to pay off the loan in 20 years instead of 25. Currently, the monthly payment is $917.25 and the loan balance is $112,247.47.
To calculate the new monthly payment for a 20-year term, we'll first determine the number of months in 20 years.
Number of months in 20 years = 20 years x 12 months/year = 240 months
Next, we divide the loan balance by the number of months to find the new monthly payment:
New monthly payment = Loan balance / Number of months
New monthly payment = $112,247.47 / 240 = $467.70 (approximately)
Now, we calculate the additional money needed by subtracting the new monthly payment from the current monthly payment:
Additional money needed = New monthly payment - Current monthly payment
Additional money needed = $467.70 - $917.25 = -$449.55
Based on the calculations, it appears that you would actually have $449.55 less in monthly expenses if you switched to a 20-year loan term. However, since you mentioned that you currently have less than $100 left over, it might not be reasonable to add the additional money needed to pay off the loan in 20 years. It's important to prioritize your financial stability and ensure you have enough savings and emergency funds.
Moving on to question 2, we need to determine the highest interest rate at which you could refinance the loan and still have a monthly total payment less than your current total payment.
First, let's calculate the current total payment by adding the escrow payment, principal and interest payment:
Current total payment = Escrow payment + Principle and Interest payment
Current total payment = $211.13 + $706.12 = $917.25
Let's assume that the new interest rate after refinancing is "x%". We can find the new monthly payment using the loan balance and the new interest rate.
New monthly payment = New principle and interest payment + Escrow payment
To find the new principle and interest payment, we subtract the escrow payment from the total payment:
New principle and interest payment = Current total payment - Escrow payment
New principle and interest payment = $917.25 - $211.13 = $706.12 (same as the current payment)
Now, we can calculate the new loan balance using the new monthly payment and the new interest rate:
New loan balance = (New monthly payment - Escrow payment) / Monthly interest rate
New loan balance = ($706.12 - $211.13) / (x% / 12)
To determine the interest rate that would require a monthly total payment less than the current total payment, we need to find the highest x% that satisfies this condition:
New total payment = New principle and interest payment + Escrow payment
New total payment = $706.12 + $211.13 = $917.25 (same as the current total payment)
Substituting the values into the equation:
$917.25 = $706.12 + $211.13
This equation shows that the escrow payment will remain constant regardless of the interest rate. Therefore, the interest rate does not affect the total payment.
Refinancing at a lower interest rate may still be beneficial in terms of reducing the interest paid over time, but it would not lower your total monthly payment. However, it's important to consider the upfront closing costs of refinancing as well.