You have purchased a house and have obtained a 30-year, $ 200,000 mortgage with an interest rate of 10%. What is your annual payment? Assuming you bought the house on January 1, what is the principal after one year? ten years?
10%??? Holy smoke! I'd be shopping around for a different lender!
http://www.interest.com/
That is the problem with old textbooks.
Secondly, who pays annual mortgage payments?
anyway ...
200000= payment(1 - 1.1^-10)/.1
solve for "payment"
For principal after one year
= 200000(1.1) - (payment)
To calculate the annual payment and the principal amount after one year and ten years, we can use the formula for calculating mortgage payments and remaining loan balance.
The formula for calculating the annual mortgage payment is:
P = (PV × r) / (1 - (1 + r)^(-n))
where:
P = annual payment
PV = present value or loan amount ($200,000)
r = monthly interest rate (10% / 12 = 0.00833)
n = number of payments in years (30)
Using this formula, we can calculate the annual payment as follows:
P = (200,000 × 0.00833) / (1 - (1 + 0.00833)^(-30)) = $21,236.58 (approx.)
Therefore, your annual payment for the mortgage is approximately $21,236.58.
To calculate the principal amount remaining after one year, we need to find the outstanding loan balance after one year. After one year, you would have made 12 monthly payments, reducing the principal balance for each payment.
To determine the principal balance at the end of one year, we can use an amortization schedule or a loan calculator with an amortization feature. However, for the sake of simplicity, let's make some estimates:
Assuming the annual payment is made at the end of each month, we can calculate the monthly payment as follows:
Monthly payment = Annual payment / 12
Monthly payment = $21,236.58 / 12 = $1,769.71 (approx.)
Now, subtracting the monthly payment for each month from the remaining balance:
Principal after one year = $200,000 - (12 × $1,769.71) = $179,255.68 (approx.)
Therefore, the principal amount after one year would be approximately $179,255.68.
To calculate the principal amount after ten years, we will use the same approach. The number of payments will be multiplied by 10.
Principal after ten years = $200,000 - (120 × $1,769.71) = $20,068.12 (approx.)
Therefore, the principal amount after ten years would be approximately $20,068.12.