Determine the regular payment amount, rounded to the nearest dollar.
The price of a home is $160,000. the bank requires a 15% down payment. The buyer is offered two mortgage options: 1 year fixed at 8% or 30-year fixed at 8%. Calculate the amount of interest paid for each option. how much does the buyer save in interest with the 15-year option?
I tried the loan calculator it didn't work
This question does not make sense to me.
"Calculate the amount of interest paid for each option" -- over what period of time ?
"how much does the buyer save in interest with the 15-year option? " -- you don't describe the 15-year option.
To calculate the regular payment amount, we first need to determine the loan amount.
The down payment required by the bank is 15% of the home price, which is $160,000. So the down payment amount is 0.15 * $160,000 = $24,000.
Therefore, the loan amount will be the difference between the home price and the down payment: $160,000 - $24,000 = $136,000.
Option 1: 1 year fixed at 8%
To calculate the monthly payment for a 1-year fixed mortgage, we need to know the interest rate and the loan term in months.
The interest rate given is 8%. To calculate the monthly interest rate, we divide it by 12 (number of months in a year): 8% / 12 = 0.0067.
The loan term is 1 year, which means 12 months.
To calculate the monthly payment, we can use the formula for a fixed-rate mortgage payment:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
- P is the monthly payment
- r is the monthly interest rate
- A is the loan amount
- n is the total number of payments (loan term in months)
Plugging in the values, we have:
P = (0.0067 * $136,000) / (1 - (1 + 0.0067)^(-12))
Calculating this using a calculator or spreadsheet software, we find that the monthly payment is approximately $11,655. Round this to the nearest dollar, and we get $11,656.
Option 2: 30-year fixed at 8%
For the 30-year fixed mortgage, the calculations are similar, except that the loan term is longer.
The monthly interest rate remains the same: 8% / 12 = 0.0067.
The loan term in months will be 30 years * 12 months/year = 360 months.
Using the same formula as before, we find:
P = (0.0067 * $136,000) / (1 - (1 + 0.0067)^(-360))
Calculating this, we find that the monthly payment is approximately $997.
Amount of interest paid for each option:
To calculate the total interest paid over the loan term, we need to subtract the loan amount from the total payments made.
For the 1-year fixed option, the total payment made over the year is $11,656 * 12 = $139,872. Therefore, the total interest paid is $139,872 - $136,000 = $3,872.
For the 30-year fixed option, the total payment made over the 30 years is $997 * 360 = $358,920. Therefore, the total interest paid is $358,920 - $136,000 = $222,920.
Amount saved in interest with the 15-year option:
To calculate the amount saved in interest with the 15-year option, we need to subtract the total interest paid with the 15-year option from the total interest paid with the 30-year option.
Amount saved = Total interest paid (30-year option) - Total interest paid (15-year option)
Amount saved = $222,920 - $3,872 = $219,048.
Therefore, the buyer saves $219,048 in interest with the 15-year option compared to the 30-year option.