You have just applied for a 30-year $100,000
mortgage at a rate of 10%. What must the annual payment be?
To calculate the annual payment for a 30-year mortgage at a rate of 10%, we can use the formula for the present value of an ordinary annuity.
PV = P * (1 - (1 + r)^(-n)) / r
Where:
PV = Present value or principal amount of the loan ($100,000)
P = Payment amount
r = Interest rate per period (10% or 0.10)
n = Number of periods (30 years or 30)
Rearranging the formula to solve for the annual payment amount (P) gives us:
P = PV * r / (1 - (1 + r)^(-n))
Substituting the given values:
P = $100,000 * 0.10 / (1 - (1 + 0.10)^(-30))
Calculating this expression:
P ≈ $11,448.87
Therefore, the annual payment for a 30-year $100,000 mortgage at a rate of 10% should be approximately $11,448.87.
To calculate the annual payment for a mortgage, we can use the formula for calculating the payment amount of a fixed-rate mortgage. The formula is:
A = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
A = Annual payment
P = Loan amount (in this case, $100,000)
r = Monthly interest rate (10% divided by 12 months, so 0.10/12 = 0.00833)
n = Total number of payments (30 years multiplied by 12 months, so 30 * 12 = 360)
Now, let's substitute the values into the formula and calculate the annual payment:
A = 100,000 * (0.00833 * (1 + 0.00833)^360) / ((1 + 0.00833)^360 - 1)
Calculating this expression, the annual payment for a 30-year $100,000 mortgage at a 10% interest rate is approximately $13,222.50.
To calculate the annual payment for a mortgage, you can use the formula for an ordinary annuity:
PMT = PV * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
PMT is the annual payment
PV is the present value or the loan amount ($100,000 in this case)
r is the interest rate per period (10% or 0.10 as a decimal)
n is the total number of periods (30 years or 30)
Using this formula, we can calculate the annual payment for the given mortgage:
PMT = 100,000 * (0.10 * (1 + 0.10)^30) / ((1 + 0.10)^30 - 1)
Let's calculate:
PMT = 100,000 * (0.10 * (1.10)^30) / ((1.10)^30 - 1)
PMT = 100,000 * (0.10 * 16.1054) / (16.1054 - 1)
PMT = 100,000 * 1.61054 / 15.1054
PMT = $10,000.00 / 15.1054
PMT ≈ $662.79 (rounded to the nearest cent)
Therefore, the annual payment for a 30-year $100,000 mortgage at a rate of 10% should be approximately $662.79.