Mr. Smith is purchasing a $190000 house. The down payment is 20% of the price of the house.
He is given the choice of:
(A) a 20-year mortgage at a rate of 6%.
Find:
(i) The monthly payment: $
(ii) The total amount of interest paid: $
To find the monthly payment and the total amount of interest paid, we first need to calculate the loan amount and the number of payments.
(i) Loan Amount:
The down payment is 20% of the price of the house, which is $190,000. So, the down payment is 0.20 * $190,000 = $38,000.
The loan amount is the price of the house minus the down payment, which is $190,000 - $38,000 = $152,000.
(ii) Number of Payments:
Since it is a 20-year mortgage, the number of payments will be 20 * 12 = 240 payments.
Next, we can use the loan amount, interest rate, and number of payments to calculate the monthly payment using the formula for a fixed-rate mortgage:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))
Where:
Loan Amount is $152,000
Interest Rate is 6% per year, which is 6 / 100 = 0.06 per year
Monthly Interest Rate is the yearly interest rate divided by 12 months, which is 0.06 / 12 = 0.005
Plugging in these numbers into the formula:
Monthly Payment = ($152,000 * 0.005) / (1 - (1 + 0.005)^(-240))
Calculating this equation will give us the monthly payment.
Next, to calculate the total amount of interest paid, we can multiply the monthly payment by the number of payments and subtract the loan amount:
Total Amount of Interest Paid = (Monthly Payment * Number of Payments) - Loan Amount
By following these steps and performing the calculations, you can find both the monthly payment and the total amount of interest paid for Mr. Smith's mortgage.
To find the monthly payment on a mortgage, we can use the formula:
M = P [i(1 + i)^n] / [(1 + i)^n - 1]
where:
M = monthly payment
P = principal amount (original loan amount)
i = monthly interest rate (annual interest rate divided by 12)
n = number of monthly payments
Given:
P = $190,000
Down payment = 20% of P
Loan amount = P - (Down payment) = 190,000 - (0.2 * 190,000) = $152,000
(i) To find the monthly payment:
Term of the mortgage = 20 years = 20 * 12 = 240 months
Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005
Applying the formula:
M = 152,000 [0.005(1 + 0.005)^240] / [(1 + 0.005)^240 - 1]
M = 152,000 [0.005(1.005)^240] / [(1.005)^240 - 1]
Using a financial calculator or spreadsheet, the monthly payment is approximately $1,235.69.
(ii) To find the total amount of interest paid:
Total amount paid = Monthly payment * Number of monthly payments
Total amount of interest paid = Total amount paid - Principal
Total amount of interest paid = (Monthly payment * Number of monthly payments) - Principal
Total amount of interest paid = ($1,235.69 * 240) - $152,000
Using a financial calculator or spreadsheet, the total amount of interest paid is approximately $196,564.60.
P = (Po*r*t)/(1-(1+r)^-t).
r = (6%/12) / 100% = 0.005 = Monthly %
rate expressed as a decimal.
t = 12mo/yr * 20yrs = 240 Months.
Po = 0.8 * 190,00 = $152,000.
P=(152000*0.005*240) / (1-(1.005)^-240
= 182400 / 0.69790 = $261,354.05
Monthly(I+P) = 261,354.05/240 = $1088.98.
Int. = P - Po = 261,354.05 - 152,000 =
$109,354.05.