Questions: Suppose that 10 years ago you bought a home for 110,000, paying 10% as a downpayment, and financing the rest at 9% interest for 30 years. This year, you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have 88,536 left to pay on your loan. Your house is now valued at 150,000. i. How much of the loan have you paid off? (i.e., how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.) ii. How much money have you paid to the loan company so far? iii. How much interest have you paid so far? iv. How much equity do you have in your home (equity is value minus remaining debt)

Suppose that 10 years ago you bought a home for 110,000, paying 10% as a downpayment, and financing the rest at 9% interest for 30 years.
This year, you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have 88,536 left to pay on your loan. Your house is now valued at 150,000.
i. How much of the loan have you paid off? (i.e., how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.)
ii. How much money have you paid to the loan company so far?
iii. How much interest have you paid so far?
iv. How much equity do you have in your home (equity is value minus remaining debt)

Transcript text: Suppose that 10 years ago you bought a home for $\$ 110,000$, paying $10 \%$ as a downpayment, and financing the rest at $9 \%$ interest for 30 years. This year, you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have $\$ 88,536$ left to pay on your loan. Your house is now valued at $\$ 150,000$. i. How much of the loan have you paid off? (i.e., how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.) ii. How much money have you paid to the loan company so far? iii. How much interest have you paid so far? iv. How much equity do you have in your home (equity is value minus remaining debt)

Solution

Solution Steps

Solution Approach

i. To find out how much of the loan has been paid off, subtract the current loan balance from the original loan amount (after the downpayment).

ii. To calculate the total amount paid to the loan company so far, determine the monthly payment using the loan amount, interest rate, and loan term, then multiply by the number of payments made (10 years).

iii. To find out how much interest has been paid so far, subtract the amount paid off from the total amount paid to the loan company.

Step 1: Calculate the Original Loan Amount

The original home price is $ \$110,000 $. The downpayment is $ 10\% $ of the home price: \[ \text{Downpayment} = 0.10 \times 110000 = 11000 \] Thus, the original loan amount is: \[ \text{Original Loan Amount} = 110000 - 11000 = 99000 \]

Step 2: Calculate the Amount of the Loan Paid Off

The current loan balance is $ \$88,536 $. The amount of the loan that has been paid off is: \[ \text{Loan Paid Off} = 99000 - 88536 = 10464 \]

Step 3: Calculate the Total Payments Made

The monthly payment can be calculated using the formula for an amortizing loan: \[ \text{Monthly Payment} = \frac{99000 \times \frac{0.09}{12}}{1 - \left(1 + \frac{0.09}{12}\right)^{-360}} \approx 796.5764 \] The total payments made over $ 10 $ years (or $ 120 $ months) is: \[ \text{Total Payments Made} = 796.5764 \times 120 \approx 95589.1669 \]

Step 4: Calculate the Interest Paid So Far

The interest paid so far can be calculated by subtracting the amount paid off from the total payments made: \[ \text{Interest Paid} = 95589.1669 - 10464 \approx 85125.1669 \]