The price of a home is $185,000. A down payment of 10% is required with 2 points at the time of closing. The home is financed over a 25 year period with a fixed rate of 4.5%. Find the monthly payment and total interest paid?
% Financed = 100%-10% = 90%.
Po = 0.9 * 185000=$166500=Amt. Financed
P = Po(1+r)^n.
r = (4.5%/12)/100% = 0.00375 = Monthly %
rate expressed as a decimal.
n = 12Comp./yr * 25Yrs = 300 Compounding
periods.
Plug the above values into the given Eq and get:
P = $511,778.13.
I = P-Po
To find the monthly payment and total interest paid for the financed home, we can use the formula for calculating the monthly payment on a fixed-rate mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ],
where:
M = Monthly payment
P = Principal amount (loan amount)
i = Monthly interest rate (annual interest rate / 12)
n = Total number of monthly payments (loan term in years * 12)
1. Calculating the down payment:
The down payment is 10% of the home price:
Down payment = 10% of $185,000
Down payment = 0.10 * $185,000
Down payment = $18,500
2. Calculating the loan amount (principal):
The loan amount is the total price of the home minus the down payment:
Principal amount = Total price - Down payment
Principal amount = $185,000 - $18,500
Principal amount = $166,500
3. Calculating the monthly interest rate:
The annual interest rate is 4.5%, so the monthly interest rate is:
Monthly interest rate = 4.5% / 12
Monthly interest rate = 0.045 / 12
Monthly interest rate = 0.00375
4. Calculating the total number of monthly payments:
The loan term is 25 years, so the total number of monthly payments is:
Total number of monthly payments = Loan term (in years) * 12
Total number of monthly payments = 25 * 12
Total number of monthly payments = 300
5. Calculating the monthly payment:
Using the formula mentioned above, we can calculate the monthly payment:
M = $166,500 [ 0.00375(1 + 0.00375)^300 ] / [ (1 + 0.00375)^300 – 1 ]
Calculating this formula will give you the monthly payment.
6. Calculating the total interest paid:
The total interest paid can be calculated by subtracting the principal amount from the total amount repaid over the loan term:
Total interest paid = (Monthly payment * Total number of monthly payments) - Principal amount
Calculating this equation will give you the total interest paid.
Please note that depending on the exact rounding and compounding methods used by lenders, there might be slight differences in the final calculated values.