You take out a 30 year $100000 mortgage loan with an apr of 6% and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principle balance on the loan?
To find the remaining principal balance on the loan after 12 years, we'll need to calculate the number of monthly payments made and subtract that from the original loan amount. Here are the steps to find the principal balance:
Step 1: Calculate the total number of monthly payments made in 12 years.
Since there are 12 months in a year and the loan term is 30 years, multiply the number of years by 12 to find the total number of months:
12 years * 12 months/year = 144 months
Step 2: Calculate the monthly interest rate.
Divide the annual percentage rate (APR) by 12 to get the monthly interest rate:
6% APR / 12 = 0.5% monthly interest rate
Step 3: Calculate the monthly payment using the loan details.
We don't have the exact monthly payment amount, but we can calculate it using a loan payment formula. The formula for calculating the monthly payment is as follows:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))
Let's calculate the monthly payment assuming a $100,000 loan amount:
Monthly Payment = ($100,000 * 0.005) / (1 - (1 + 0.005)^(-360))
Monthly Payment ≈ $599.55 (round to the nearest cent)
Step 4: Calculate the remaining principal balance.
To find the remaining principal balance after 12 years, multiply the monthly payment by the number of payments made and subtract this total from the loan amount:
Remaining Principal Balance = Loan Amount - (Monthly Payment * Number of Payments Made)
Remaining Principal Balance = $100,000 - ($599.55 * 144)
Remaining Principal Balance ≈ $18,745.20 (round to the nearest cent)
Therefore, the remaining principal balance on the mortgage loan after 12 years is approximately $18,745.20.
To find the remaining balance on the mortgage loan after 12 years, we need to determine the monthly payment amount and calculate the number of remaining payments.
1. Calculate the monthly interest rate: The annual percentage rate (APR) is given as 6%. To find the monthly interest rate, divide it by 12 (months).
Monthly interest rate = APR / 12 = 6% / 12 = 0.005.
2. Calculate the number of remaining payments: Since you have been paying for 12 years already on a 30-year loan, there are 30 - 12 = 18 years remaining on the loan. Multiply this by 12 to get the number of remaining monthly payments.
Number of remaining payments = Remaining years × 12 = 18 × 12 = 216 months.
3. Calculate the monthly payment: To calculate the monthly payment, we can use the formula for the present value of an ordinary annuity.
PMT = P × (r × (1+r)^n) / ((1+r)^n - 1),
Where:
PMT = Monthly payment
P = Principal amount of the loan ($100,000)
r = Monthly interest rate (0.005)
n = Number of remaining payments (216)
PMT = 100,000 × (0.005 × (1+0.005)^216) / ((1+0.005)^216 - 1).
Calculating PMT will give us the monthly payment amount.
4. Calculate the remaining balance: Finally, we need to find the remaining balance on the loan. Multiply the monthly payment by the number of remaining payments.
Remaining balance = PMT × Number of remaining payments.
Plug in the values obtained from the previous steps to calculate the remaining balance on the loan after 12 years.