The price of a small cabin is $55,000. 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? Find the monthly payment for the 20-year option.
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The price of a small cabin is $45 comma 00045,000. 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?
To calculate the amount of interest paid for each mortgage option, we need to determine the loan amount and the total payments made over the term of the loan.
1. Loan Amount:
The down payment required by the bank is 5% of the price of the cabin, which is $55,000.
Down payment = 5% * $55,000 = $2,750
The loan amount is the remaining price after the down payment.
Loan amount = $55,000 - $2,750 = $52,250
2. Total Payments:
For the 20-year option:
Number of monthly payments = 20 years * 12 months = 240 months
For the 30-year option:
Number of monthly payments = 30 years * 12 months = 360 months
Now, we can calculate the amount of interest paid for each option.
For the 20-year option:
Interest rate = 7.5%
Total interest paid = (Loan amount) * (Interest rate) * (Number of monthly payments)
Total interest paid = $52,250 * 0.075 * 240 = $936,750
For the 30-year option:
Interest rate = 7.5%
Total interest paid = (Loan amount) * (Interest rate) * (Number of monthly payments)
Total interest paid = $52,250 * 0.075 * 360 = $1,405,500
To find the amount saved in interest with the 20-year option:
Interest saved = Total interest paid for the 30-year option - Total interest paid for the 20-year option
Interest saved = $1,405,500 - $936,750 = $468,750
As for the monthly payment for the 20-year option, we can use the formula for calculating the monthly payment for a fixed-rate mortgage:
Monthly payment = (Loan amount) * (Monthly interest rate) / (1 - (1 + Monthly interest rate) ^ (-Number of monthly payments))
Monthly interest rate = (Annual interest rate) / 12
Monthly interest rate = 7.5% / 12 = 0.00625
Monthly payment = $52,250 * 0.00625 / (1 - (1 + 0.00625) ^ (-240))
Monthly payment ≈ $421.19
So, the monthly payment for the 20-year fixed option is approximately $421.19.
To calculate the amount of interest paid for each mortgage option, we need to determine the loan amount, calculate the total payment, and then subtract the initial price of the cabin from the total payment.
First, let's calculate the loan amount by subtracting the down payment from the price of the cabin:
Down payment = 5% of $55,000 = 0.05 * $55,000 = $2,750
Loan amount= Price of the cabin - Down payment = $55,000 - $2,750 = $52,250
To calculate the total payment for each mortgage option, we'll use the formula for the monthly payment of a fixed-rate mortgage:
Total Payment = Monthly Payment * Total Number of Payments
Now, let's calculate the total payment for the 20-year option:
Total Number of Payments = 20 years * 12 months per year = 240 months
Monthly Interest Rate = 7.5% / 100 / 12 = 0.075 / 12 = 0.00625
Monthly Payment = Loan amount * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Total Number of Payments)))
= $52,250 * (0.00625 / (1 - (1 + 0.00625)^(-240)))
≈ $432.93
Total Payment = Monthly Payment * Total Number of Payments = $432.93 * 240 = $103,903.20
Now, let's calculate the total payment for the 30-year option:
Total Number of Payments = 30 years * 12 months per year = 360 months
Monthly Interest Rate = 7.5% / 100 / 12 = 0.075 / 12 = 0.00625
Monthly Payment = Loan amount * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Total Number of Payments)))
= $52,250 * (0.00625 / (1 - (1 + 0.00625)^(-360)))
≈ $366.97
Total Payment = Monthly Payment * Total Number of Payments = $366.97 * 360 = $132,109.20
To calculate the amount of interest paid for each option, we subtract the price of the cabin from the total payment:
Interest Paid (20-year option) = Total Payment - Price of the cabin
= $103,903.20 - $55,000 = $48,903.20
Interest Paid (30-year option) = Total Payment - Price of the cabin
= $132,109.20 - $55,000 = $77,109.20
To find how much the buyer saves in interest with the 20-year option, we subtract the interest paid for the 20-year option from the interest paid for the 30-year option:
Savings in interest = Interest Paid (30-year option) - Interest Paid (20-year option)
= $77,109.20 - $48,903.20 = $28,206.00
To calculate the monthly payment for the 20-year option, we already determined it to be approximately $432.93.