These problems do not focus on complicated hand mortgage calculation, but focus on the role of principal and interest in the math behind a mortgage.
1.
A person takes out a loan for a home. The home costs $240,000.
They will not have a down payment. The monthly payments are $1,597 per
month. The monthly payment does not include taxes, insurance, etc. The
loan is for 30 years. The interest rate is 7%.
How much money will the person end up paying if they make no early/extra payments and pay off the mortgage in the full course of the loan, 30 years?
This person is paying $1,597 per month for 30 years. That means the total amount they will pay is
\[\$1,597 \cdot 12 \text{ months} \cdot 30 \text{ years} = \$574,920\]
2.
A person takes out a loan for a home. The home costs $240,000.
They will not have a down payment. The monthly payments are $1,597 per
month. The monthly payment does not include taxes, insurance, etc. The
loan is for 30 years. The interest rate is 7%.
How much of their money will go to interest if they make no early/extra payments?
Above, we calculated how much this person will pay by the end of the loan. If the principal/starting amount is $240,000, then they have paid
\[\$574,920 - \$240,000 = \$334,920\]
in interest.
3.
If the person above decides to make a down payment of 20%, how
much will their down payment be?
If the home costs $240,000, a 20% down payment would be
\[\$240,000 \cdot 0.20 = \$48,000\]
4.
If the person above makes a down payment when purchasing a home,
their new loan is for $192,000. Their monthly payments are now $1,277.
The loan is still for 30 years at 7% interest. How much money will they
spend on interest in this loan? How much interest did they save over the
course of the loan as compared to the loan with now down payment?
If they pay $1,277 per month for 30 years, they will spend
\[\$1,277 \cdot 12 \text{ months} \cdot 30 \text{ years} = \$459,720\]
total for the home. That means they pay
\[\$459,720 - \$192,000 = \$267,720\]
in interest. Compared to the interest of the non-down payment loan, the interest they save is
\[\$334,920 - \$267,720 = \$67,200\]
5.
A home loan has a monthly payment of $1,597 per month. The amount
they still owe (the principal) is $240,000 at the time of the first
payment. The interest rate is 7%. Calculate the amount of their $1,597
monthly payment that has to go to interest.
7% interest is a yearly rate. To calculate the amount of interest they owe after their first payment, we will divide the yearly 7% interest by 12 to convert it to the monthly interest they owe.
\[\text{interest owed } = \$240,000 \cdot \frac{0.07}{12} \approx \$1,400\]
This person paid $1,597 for their monthly payment, but the total amount they owe (the principal) has only gone down by $1,597 - $1,400 = $197
1. A person takes out a loan for a home. The home costs $280,000. They will not have a down payment. The monthly payments are $1,936 per month. The monthly payment does not include taxes, insurance, etc. The loan is for 30 years. The interest rate is 7.4%.
2. A person takes out a loan for a home. The home costs $280,000. They will not have a down payment. The monthly payments are $1,936 per month. The monthly payment does not include taxes, insurance, etc. The loan is for 30 years. The interest rate is 7.4%.
How much of their money will go to interest if they make no early/extra payments?
3. If the person above decides to make a down payment of 20%, how much will their down payment be?
4. If the person above makes a down payment when purchasing a home, their new loan is for $224,000. Their monthly payments are now $1,549. The loan is still for 30 years at 7.4% interest. How much money will they spend on interest in this loan? How much interest did they save over the course of the loan as compared to the loan with now down payment?
5. A home loan has a monthly payment of $1,936 per month. The amount they still owe (the principal) is $280,000 at the time of the first payment. The interest rate is 7.4%. Calculate the amount of their $1,936 monthly payment that has to go to interest.
6. Halfway through the above loan, at year 15, the person still owes $210,418.007 on the principal. The interest rate is 7.4%. How much of their $1,936 monthly payment goes to interest at this point in the loan?
1. After one year, a certain percentage of the monthly payment goes to interest. After ten years, a lower percentage of the monthly payment goes to interest. After twenty years, an even lower percentage of the monthly payment goes to interest. What is the relationship between time and interest on the loan? Is it linear, exponential, etc.?
2. What are things that homeowners can do to reduce the amount of interest that a homeowner pays?