The price of a small cabin is $45,000. The bank requires a 5% down payment. The buyer is offered two mortgage options: 20-year fixed at 6.56.5% or 30-year fixed at 6.56.5%. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 20-year option?
All kinds of problems with this question.
It is invalid to compare "interest paid" when you don't have the same focal dates.
Are there monthly payments?
I sure hope you weren't thinking of using simple interest.
Since the interest rates are the same, the interest paid is the same.
To calculate the amount of interest paid for each mortgage option and the amount saved with the 20-year option, we need to use the formulas for calculating mortgage payments and interest.
First, let's calculate the mortgage payment for each option using the loan amount. To find the loan amount, we subtract the down payment from the cabin price.
Loan Amount = Cabin Price - Down Payment
Loan Amount = $45,000 - (5% * $45,000) = $45,000 - $2,250 = $42,750
Now let's calculate the mortgage payment for the 20-year fixed option. We will use the formula:
Mortgage Payment = Loan Amount * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Number of Payments)))
Monthly Interest Rate = Annual Interest Rate / 12
Number of Payments = Number of Years * 12
For the 20-year fixed option:
Monthly Interest Rate = 6.5% / 12 = 0.065 / 12 = 0.00542
Number of Payments = 20 * 12 = 240
Mortgage Payment = $42,750 * (0.00542 / (1 - (1 + 0.00542)^(-240)))
Mortgage Payment ≈ $294.98
Next, let's calculate the mortgage payment for the 30-year fixed option. We will use the same formulas but adjust the number of payments.
For the 30-year fixed option:
Number of Payments = 30 * 12 = 360
Mortgage Payment = $42,750 * (0.00542 / (1 - (1 + 0.00542)^(-360)))
Mortgage Payment ≈ $267.92
To calculate the total interest paid for each option, we can subtract the loan amount from the total amount paid over the term of the mortgage.
Total Payments = Mortgage Payment * Number of Payments
Total Interest Paid = Total Payments - Loan Amount
For the 20-year fixed option:
Total Payments = $294.98 * 240 ≈ $70,795.20
Total Interest Paid = $70,795.20 - $42,750 ≈ $28,045.20
For the 30-year fixed option:
Total Payments = $267.92 * 360 ≈ $96,451.20
Total Interest Paid = $96,451.20 - $42,750 ≈ $53,701.20
Now to calculate the amount saved with the 20-year option, we subtract the total interest paid for the 20-year option from the total interest paid for the 30-year option.
Amount Saved = Total Interest Paid (30-year option) - Total Interest Paid (20-year option)
Amount Saved = $53,701.20 - $28,045.20 ≈ $25,656.00
Therefore, the buyer saves approximately $25,656.00 in interest by choosing the 20-year fixed option instead of the 30-year fixed option.