in terms of paying less in interest, which is more economical for a $230,000 mortgage: a 30 year fixed-rate at 9% or a 20 year fixed-rate at 8.5%? How much is saved in interest?
Without even doing the math, it is obvious that a longer term at a higher interest will cost much more in interest.
To determine which mortgage is more economical in terms of paying less interest, we need to compare the total interest paid for each option.
Let's start by calculating the total interest paid for the 30-year fixed-rate mortgage at 9% interest.
Step 1: Calculate the monthly interest rate.
Monthly Interest Rate = Annual Interest Rate / 12
Monthly Interest Rate = 9% / 12 = 0.75%
Step 2: Calculate the total number of months.
Total Number of Months = Loan Term in Years * 12
Total Number of Months = 30 * 12 = 360 months
Step 3: Calculate the monthly payment using the loan amount, interest rate, and loan term.
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Total Number of Months))
Monthly Payment = (230,000 * 0.0075) / (1 - (1 + 0.0075)^-360)
Now, let's calculate the total interest paid for the 20-year fixed-rate mortgage at 8.5% interest.
Step 1: Calculate the monthly interest rate.
Monthly Interest Rate = Annual Interest Rate / 12
Monthly Interest Rate = 8.5% / 12 = 0.7083%
Step 2: Calculate the total number of months.
Total Number of Months = Loan Term in Years * 12
Total Number of Months = 20 * 12 = 240 months
Step 3: Calculate the monthly payment using the loan amount, interest rate, and loan term.
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Total Number of Months))
Monthly Payment = (230,000 * 0.007083) / (1 - (1 + 0.007083)^-240)
To determine how much is saved in interest, we need to find the difference in total interest paid between the two mortgages.
Total Interest Paid = (Monthly Payment * Total Number of Months) - Loan Amount
For the 30-year fixed-rate mortgage:
Total Interest Paid = (Monthly Payment * 360) - 230,000
For the 20-year fixed-rate mortgage:
Total Interest Paid = (Monthly Payment * 240) - 230,000
By subtracting the total interest paid for the 20-year mortgage from the total interest paid for the 30-year mortgage, you can find out how much is saved in interest by choosing the 20-year option.