The price of a small cabin is $35,000. The bank requires a 5% down payment. The buyer is offered two mortgage options: 20-year fixed at 7.5% or 30-year fixed at 7.5%. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 20-year option?
20-year fixed:
P = Po*r*t/(-(1+r)^-t).
Po = 35000*0.95 = $33,250.
r = (7.5%/12)/100% = 0.00625 = Monthly %rate expressed as a decimal.
t = 20yrs. * 12mo./yr. = 240 Months.
P1 = 33,250*0.00625/(1-1.00625^-240) =
$64,286.34.
I = P1-Po=64,286.34-33,250=$31,036.34.
30-year fixed:
Use same procedure as 20-year fixed.
To calculate the down payment, we need to find 5% of the purchase price:
5% of $35,000 = $35,000 * 0.05 = $1,750
For both mortgage options, we should calculate the loan amount by subtracting the down payment from the purchase price:
Loan amount = Purchase price - Down payment
Loan amount = $35,000 - $1,750 = $33,250
Next, let's calculate the total interest paid for each mortgage option.
For the 20-year fixed mortgage option:
Interest rate = 7.5%
Loan term = 20 years
Loan amount = $33,250
To calculate the total interest paid, we can use the following formula:
Total interest paid = (Loan amount * Interest rate * Loan term) / 100
Total interest paid = ($33,250 * 7.5 * 20) / 100 = $49,875
For the 30-year fixed mortgage option:
Interest rate = 7.5%
Loan term = 30 years
Loan amount = $33,250
Total interest paid = (Loan amount * Interest rate * Loan term) / 100
Total interest paid = ($33,250 * 7.5 * 30) / 100 = $74,625
Therefore, the buyer saves in interest with the 20-year option is:
Interest savings = Total interest paid for 30-year option - Total interest paid for 20-year option
Interest savings = $74,625 - $49,875 = $24,750
To calculate the amount of interest paid for each mortgage option, we need to determine the loan amount and the total payment over the specified term. Let's start with the 20-year fixed mortgage:
1. Loan Amount: The down payment is calculated as a percentage of the total price. In this case, the down payment is 5% of $35,000, which is 0.05 * $35,000 = $1,750. Therefore, the loan amount for the 20-year option is $35,000 - $1,750 = $33,250.
2. Monthly Payment: To calculate the monthly payment, we use the formula for a fixed-rate mortgage:
Monthly Payment = Loan Amount * (Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-total number of payments))
First, we convert the annual interest rate to a monthly interest rate. In this case, the annual interest rate is 7.5%, so the monthly interest rate is 7.5% / 12 = 0.625%.
Next, we calculate the total number of payments, which is the number of years multiplied by the number of payments per year. In this case, it's 20 years * 12 months = 240 payments.
Finally, we plug in the values into the formula:
Monthly Payment = $33,250 * (0.00625) / (1 - (1 + 0.00625)^(-240))
Calculating this gives us the monthly payment for the 20-year option.
3. Total Payment: To calculate the total payment over the 20-year term, we multiply the monthly payment by the total number of payments:
Total Payment = Monthly Payment * total number of payments
Calculating this gives us the total payment for the 20-year option.
To calculate the interest paid for the 30-year fixed mortgage:
1. Loan Amount: The loan amount for the 30-year option is the same as the 20-year option, which is $33,250.
2. Monthly Payment: We use the same formula to calculate the monthly payment as we did for the 20-year option. The only difference is the total number of payments, which is now 30 years * 12 months = 360 payments.
3. Total Payment: We multiply the monthly payment by the total number of payments to calculate the total payment over the 30-year term.
Once we have calculated the total payment for each option, we can subtract the loan amount from the total payment to determine the total interest paid.
To find out how much the buyer saves in interest with the 20-year option, you subtract the total interest paid for the 20-year mortgage from the total interest paid for the 30-year mortgage.
Remember, the formulas provided above are the general formulas for calculating mortgage payments. Some additional factors, such as taxes, insurance, and any additional fees, may impact the final calculations.