You have just applied for a 30-year $100000 mortgage at a rate of 10%. What must the annual payment be?
Strange mortgage with annual payments?
P( 1 - 1.1^-30)/.1 = 100000
solve for P
Hey can you please help out in the other questions too... I've been stuck for a while without help!!
To calculate the annual payment for a 30-year mortgage at a rate of 10%, you need to use the formula for calculating the fixed monthly payment on a mortgage:
P = (P.V) / (1 - (1 + r)^(-n))
Where:
P = principal amount (loan amount)
V = monthly interest rate (annual interest rate divided by 12)
r = number of payments per year (12 for monthly payments)
n = total number of payments (30 years multiplied by 12 months)
Let's calculate it step-by-step:
1. Convert the annual interest rate to a monthly interest rate:
V = 10% / 12 = 0.83%
2. Calculate the number of monthly payments:
n = 30 years * 12 months = 360 months
3. Plug the values into the formula:
P = (100,000 * 0.0083) / (1 - (1 + 0.0083)^(-360))
4. Simplify the equation:
P = (830) / (1 - (1.0083)^(-360))
5. Calculate the value of (1.0083)^(-360):
(1.0083)^(-360) ≈ 0.0966
6. Plug the value into the main equation:
P = (830) / (1 - 0.0966)
7. Simplify further:
P = (830) / (0.9034)
8. Calculate the annual payment:
P ≈ $918.85
So, the annual payment on a 30-year $100,000 mortgage at a 10% interest rate would be approximately $918.85.
To calculate the annual payment for a mortgage, you can use the formula for the periodic payment of a loan, which is derived from the concepts of present value and annuity.
Here's how you can calculate the annual payment for your 30-year $100,000 mortgage at a rate of 10%:
Step 1: Convert the annual interest rate to a decimal form.
The interest rate of 10% should be divided by 100 to convert it to a decimal form. In this case, it becomes 0.10.
Step 2: Determine the number of payment periods.
In this scenario, you have a 30-year mortgage. As there are 12 months in a year, the total number of payment periods will be 30 multiplied by 12, which equals 360 months.
Step 3: Calculate the periodic interest rate.
The annual interest rate needs to be divided by the number of payment periods in a year. Since there are 12 months in a year, divide the annual interest rate (0.10) by 12. The monthly interest rate will be 0.10 / 12 = 0.00833.
Step 4: Calculate the present value factor.
The present value factor (PVF) is used to calculate the periodic payment of a loan. It can be calculated using the formula: PVF = (1 - (1 + r)^(-n)) / r, where r is the periodic interest rate and n is the number of payment periods. In this case, r is 0.00833 and n is 360. Substituting these values into the formula, you get: PVF = (1 - (1 + 0.00833)^(-360)) / 0.00833 ≈ 62.97.
Step 5: Calculate the annual payment.
The annual payment is calculated by dividing the loan amount by the present value factor. In this case, the loan amount is $100,000. So, dividing $100,000 by 62.97, you get an annual payment of approximately $1585.60.
Therefore, the annual payment for a 30-year $100,000 mortgage at a rate of 10% is approximately $1585.60.