Financial Project
Five years ago, you bought a house for $171,000. You had a down payment of $35,000, which meant you took out a loan for $136,000. Your interest rate was $5.6% fixed. You would like to pay more on your loan. You check your bank statement and find the following information.
•Escrow payment: $232.78
•Principle and Interest payment: $751.90
•Total payment: $984.68
•Current Loan balance: $121,259.44
Then, answer these questions:
1. Assuming you currently meet your monthly expenses with no left over to speak of, how much more money a month do you need to make in order to pay off your loan in 20 years instead of 25? Is this reasonable?
2. Is it more or less reasonable to consider refinancing your loan? In order to answer this, you need to look at different interest rates. Know that if you refinance, your minimum monthly payments will be based on a thirty-year loan (though you still want to be done in 20 years). 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 needed to pay off the loan in 20 years instead of 25, and compare it with the current monthly payment. We also need to calculate the cost of refinancing and determine if it would be more reasonable.
1. To calculate the monthly payment needed to pay off the loan in 20 years instead of 25, we can use the formula for the monthly payment of a fixed-rate loan:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = monthly payment
r = monthly interest rate
PV = loan balance
n = total number of payments
First, we need to calculate the monthly interest rate. The annual interest rate of 5.6% needs to be divided by 12 to get the monthly rate: 5.6% / 12 = 0.4667%.
Next, calculate the total number of payments for 20 years: 20 x 12 = 240 payments.
Now, substitute the values into the formula:
P = (0.4667% * $121,259.44) / (1 - (1 + 0.4667%)^(-240))
P ≈ $894.59
To pay off the loan in 20 years instead of 25, you would need to make an additional monthly payment of $894.59 - $751.90 = $142.69.
To determine if this is reasonable, consider your current financial situation and whether you can afford this additional monthly payment. Assess your income, expenses, and other financial obligations to determine if you can comfortably make the higher payment without sacrificing your other financial goals.
2. To determine if refinancing is more reasonable, we need to compare the costs and benefits.
Refinancing involves getting a new loan with different terms, including a new interest rate. You mentioned that refinancing costs a couple of thousand dollars in closing costs. Let's assume it costs $2,000.
Calculate the monthly payment for a 30-year loan using the new interest rate. Consider different interest rates and choose one that is feasible.
For example, let's say you find a new interest rate of 4.5% for the refinanced loan.
Using the formula mentioned earlier, calculate the new monthly payment:
P = (0.375% * $121,259.44) / (1 - (1 + 0.375%)^(-360))
P ≈ $607.27
Now, compare the new monthly payment of $607.27 with the current payment of $751.90. Calculate the difference:
$751.90 - $607.27 ≈ $144.63
In this case, refinancing would result in a slightly lower monthly payment compared to making additional payments on the current loan.
However, keep in mind that refinancing also has upfront costs of $2,000. Assess whether the potential savings in monthly payments would offset the costs of refinancing in the long run.
Consider other factors such as the total interest paid over the life of the loan, your financial goals, and how long you plan to stay in the house before making a decision on refinancing.
Ultimately, the reasonableness of refinancing depends on your personal financial situation and goals.