The Patel family recently purchased a home, taking out a mortgage of $235,000
at 8 1/2% for 25 years. Excluding taxes and insurance, what is the monthly PITI
payment of their loan?
i = .085/12 = .00708333
n = 12x25 = 300
payment = ?
paym ( 1 - 1.00708333^-300)/.00708333 = 235000
I will let you do the arithmetic.
(hope you get $1892.28)
M = P [ i ] / [ 1-(1+i)^-n]
M = Monthly Mortgage Payment
P = Mortgage Amount
i = Monthly Interest Rate.
.085/12 = .007083
n = 25*12 = 300
M = 235000[.085/12] /[1-(1+.085/12)^-300]
M = 1892.28
To calculate the monthly PITI payment, you need to consider four components: Principal, Interest, Taxes, and Insurance.
1. Principal and Interest:
To calculate the principal and interest portion of the monthly payment, you can use a loan payment formula. The formula to calculate the monthly payment is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Where:
M = Monthly payment
P = Loan amount
i = Monthly interest rate
n = Number of payments (in this case, the number of months)
For the principal and interest portion:
P = $235,000 (loan amount)
i = (8.5% / 100) / 12 (monthly interest rate)
n = 25 * 12 (number of months)
First, convert the annual interest rate to a monthly interest rate:
i = 0.085 / 12 = 0.00708333
Then, calculate the number of payments:
n = 25 * 12 = 300
Next, substitute these values into the formula and calculate the principal and interest portion:
M = $235,000 * [ 0.00708333 * (1 + 0.00708333)^300 ] / [ (1 + 0.00708333)^300 – 1 ]
2. Taxes:
To calculate the tax portion of the monthly payment, you need to know the annual property tax amount. Let's assume it's $3,000. Divide the annual property tax by 12 to get the monthly tax amount:
Monthly Tax = $3,000 / 12 = $250
3. Insurance:
Similarly, to calculate the insurance portion of the monthly payment, you need to know the annual insurance premium. Let's assume it's $1,200. Divide the annual insurance premium by 12 to get the monthly insurance amount:
Monthly Insurance = $1,200 / 12 = $100
4. Total PITI Payment:
Add up the principal and interest, tax, and insurance portions to get the total monthly PITI payment:
Total Monthly PITI Payment = Principal + Interest + Taxes + Insurance
Just substitute the calculated values into this equation to get the final answer.