You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $2825 and you have made every payment on time. The original term of the mortgage was 30 years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 6.372%(APR). How much do you owe on the mortgage today?
Part 1
The amount you owe today is $ (Round to the nearest dollar.)
To determine how much you owe on your mortgage today, we’ll need to consider the original term of your mortgage, the monthly payments you’ve been making, and the interest rate. Let’s break this down step by step:
1. Original Mortgage Term: You mentioned that the original term of your mortgage was 30 years. This means that when you initially took out the mortgage, it was set to be paid off over a 30-year period.
2. Current Mortgage Age: You also mentioned that the mortgage is exactly four years and eight months old. To calculate the number of months that have passed since you took out the mortgage, we can multiply 4 years by 12 months/year and add the 8 months. So, it has been 4 * 12 + 8 = 56 months since you got the mortgage.
3. Monthly Payment: Your current monthly payment is $2,825, and you’ve been making these payments on time.
4. Mortgage Interest Rate: The annual percentage rate (APR) of your mortgage is 6.372%.
Now, let’s calculate how much you owe on your mortgage today:
First, we need to calculate the total number of monthly payments you would make over the 30-year term of the mortgage. Since a year has 12 months, the total number of months in 30 years is 30 years * 12 months/year = 360 months.
Next, we’ll calculate how many monthly payments you have left. To do this, subtract the number of months you’ve already paid from the total number of months in the mortgage term:
Total months in the mortgage term – Months you’ve paid = 360 months – 56 months = 304 months remaining.
Now, we can calculate the remaining balance on your mortgage using the formula for the remaining balance on a fixed-rate mortgage:
Remaining Balance = P * [(1 – (1 + r)^(-n)) / r],
where:
– P is your monthly payment ($2,825),
– r is the monthly interest rate (6.372% annual rate / 12 months = 0.531% monthly rate), and
– n is the number of remaining months (304 months).
Now, let’s calculate:
Remaining Balance = $2,825 * [(1 – (1 + 0.00531)^(-304)) / 0.00531]
Remaining Balance ≈ $411,219 (rounded to the nearest dollar).
So, you owe approximately $411,219 on your mortgage today. It’s essential to note that this is an estimate, and the exact amount may vary slightly depending on the specific terms and calculations used by your mortgage lender.
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