You have just graduated from college and landed your first big job. You have always dreamed of being a homeowner, and after carefully shopping for your dream home, you find one that you would like to purchase at a cost of $250,000. After researching banks to find the best interest rate, you find that Banks for Homeowners offers the best rate of 6% interest that compounds monthly for 30 years.
•What is the monthly payment for this loan?
•What is the unpaid balance of the loan at the end of 5 years?
•What is the unpaid balance at the end of the 10th year?
y/2-5=1
Pt = (Po*r*t) / (1 - (1 + r)^-t).
Pt = Loan amount after 30 years.
Po = Amount of loan = $250,000.
r = (6% / 12) / 100 = 0.005 = Int. rate
per month expressed as a decimal.
t=lenth of loan = 30 yrs. = 360 months.
Pt=(250000*0.005*360)/(1 -(1.005)^-360,
Pt = 450000 / (1-0.16604) = $539,595.47
= Amount of loan after 30 yrs.
539595.47 / 360mo = $1498.88 = monthly
payments.
The process of calculating the balance
before the maturity date is called Amortizing and cannot be shown here
because of the length of the table involved.
I can share this INFO with you:
5-Yr. Bal: $232,691.84
Payed off 56% of a 30 year mortgage in 5years....
To calculate the monthly payment, unpaid balance at the end of 5 years, and unpaid balance at the end of the 10th year, we need to use the formula for monthly mortgage payments and the formula for calculating the unpaid balance.
1. Monthly Payment:
To calculate the monthly payment, we can use the formula for the monthly mortgage payment, which is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of months (30 years * 12 months per year)
In this case, P = $250,000, r = 6% / 12 = 0.06 / 12 = 0.005, and n = 30 * 12 = 360.
Plugging these values into the formula, we can calculate the monthly payment.
2. Unpaid Balance at the End of 5 Years:
To calculate the unpaid balance at the end of 5 years, we need to find the remaining balance after making monthly payments for 5 years. We can use the formula for the unpaid balance, which is:
B = P * (1 + r)^n - (M * ((1 + r)^n - 1) / r)
Where:
B = Unpaid balance
P = Principal amount (loan amount)
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of months (5 years * 12 months per year)
M = Monthly payment
Plugging in the values, we can calculate the unpaid balance at the end of 5 years.
3. Unpaid Balance at the End of 10 Years:
Similar to the calculation for 5 years, we can use the same formula to calculate the unpaid balance at the end of 10 years. We need to find the remaining balance after making monthly payments for 10 years. Plugging in the values, we can calculate the unpaid balance at the end of 10 years.
By using the formulas provided, you can calculate the monthly payment, unpaid balance at the end of 5 years, and unpaid balance at the end of 10 years for your dream home.