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?
Please submit your assignment.
monthly $1498.88
5yr $229553.48
10 yr $205056.61
A = 2 pi r h
solve for r
need to show all work please help
To calculate the monthly payment, unpaid balance after 5 years, and unpaid balance after 10 years, we can use the basic formula for a fixed-rate mortgage:
Monthly payment formula:
P = (Pv × r) / (1 - (1 + r)^(-n))
where:
P = Loan amount
r = Monthly interest rate
n = Total number of months
Unpaid balance after a certain duration formula:
Bal = (Pv × (1 + r)^n) - ((Pv × (1 + r)^n-1) / r)
where:
Bal = Unpaid balance
Pv = Loan amount
r = Monthly interest rate
n = Number of months
Let's plug in the values for your case:
Loan amount (P) = $250,000
Now, let's calculate the monthly interest rate (r). Since the annual interest rate is 6% and compounds monthly, we divide it by 12 to get the monthly rate:
r = (6% / 12) / 100 = 0.005
Total number of months (n) = 30 years × 12 months = 360 months
Calculating the monthly payment:
P = ($250,000 × 0.005) / (1 - (1 + 0.005)^(-360))
Using a calculator or spreadsheet, solve this equation to find the monthly payment.
To calculate the unpaid balance after 5 years:
n = 5 years × 12 months = 60 months
Bal = ($250,000 × (1 + 0.005)^60) - (($250,000 × (1 + 0.005)^59) / 0.005)
Calculate this using a calculator or spreadsheet.
To calculate the unpaid balance after 10 years:
n = 10 years × 12 months = 120 months
Bal = ($250,000 × (1 + 0.005)^120) - (($250,000 × (1 + 0.005)^119) / 0.005)
Calculate this using a calculator or spreadsheet.
Once you have the formulas and values, you can easily calculate the monthly payment, unpaid balance after 5 years, and unpaid balance after 10 years using either a calculator or a spreadsheet program.