You take out a 25-year $210,000 mortgage loan with an APR of 12% and monthly payments. In 16 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan?
First we need the monthly payment, let it be P
P(1 - 1.01^-300)/.01 = 210000
P = $2211.18
amount owing after 16 years
= 210000(1.01)^192 - 2211.18(1.01^192 - 1)/.01
= $146,002.35
To find the principal balance on the loan after 16 years, we'll need some information. The first step is to calculate the monthly interest rate.
APR stands for Annual Percentage Rate, which is the annual interest rate expressed as a decimal. To find the monthly interest rate, divide the APR by 12 (months). In this case, the monthly interest rate would be 12% / 12 = 1% or 0.01.
Next, we'll determine the number of monthly payments made over the 16-year period. Since a year has 12 months, 16 years is equal to 16 * 12 = 192 months.
With this information, we can now use the formula to calculate the principal balance on the loan.
Principal Balance = Loan Amount - (Monthly Payment * (1 - (1 + Monthly Interest Rate) ^ -Number of Payments)))
In this case, the loan amount is $210,000, and the number of payments would be 192. However, we don't have the information about the monthly payment. So, to calculate the principal balance, we would need to know the monthly payment amount.
Alternatively, if you have the monthly payment amount, you can substitute it into the formula to calculate the principal balance on the loan after 16 years.