You take out a 30-year $100,000 mortgage loan with an APR of 6 percent and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan?
I am working this on the assumption that your monthly rate is .005.
First we find our monthly payment:
100000= paym[1-(1.005)^-360]/.005
paym= 599.55
Now finding the amount of 144 of those payments
=599.55((1.005^144)-1)/.005
=125,995.64
Finding the value of our debt after 144 periods if no payments had been made
=100000(1.005^144
=205,075.08
So the outstanding balance after 12 years
= 205075.08-125995.64
=79,079.44
I hope you are familiar with the formulas I was using.
If not, please let me know and I can explain them in more detail.
Oh, familiar with the formulas? More like familiar with the circus! But don't worry, I've got the math skills to clown around with this question. So, after 12 years of your mortgage, the principal balance on the loan is $79,079.44. Time to break out the confetti and celebrate, because that's quite a chunk of change!
Yes, I am familiar with the formulas you used. To calculate the principal balance on the loan after 12 years, you correctly computed the monthly payment using the formula for a fixed-rate mortgage. Then, you calculated the total amount paid after 12 years by multiplying the monthly payment by the number of payments (144) and subtracting it from the initial loan amount.
The principal balance on the loan after 12 years is $79,079.44.
Yes, I am familiar with the formulas you used to calculate the principal balance on the mortgage loan. Let me explain the steps you took to arrive at the answer.
First, you used the formula for calculating the monthly payment on a mortgage loan. This formula is:
Payment = Loan Amount * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Number of Payments)))
In your case, the Loan Amount is $100,000, the APR is 6 percent (which translates to a monthly interest rate of 0.005), and the number of payments is 360 (30 years * 12 months). Plugging these values into the formula, you found that the monthly payment is $599.55.
Next, you calculated the total amount paid after 144 payments (12 years). To do this, you used the formula for the sum of a geometric series:
Total Amount = Monthly Payment * ((1 + Monthly Interest Rate)^Number of Payments - 1) / Monthly Interest Rate
By plugging in the values, you found that after 144 payments, the total amount paid is $125,995.64.
Finally, you determined the outstanding balance after 12 years by subtracting the total amount paid from the original loan amount. This gives you:
Outstanding Balance = Loan Amount * (1 + Monthly Interest Rate)^Number of Payments - Total Amount Paid
= $100,000 * (1.005^144) - $125,995.64
= $205,075.08 - $125,995.64
= $79,079.44
Therefore, the principal balance on the loan after 12 years is $79,079.44.
I hope this explanation helps! Let me know if you have any further questions.