What is the annual payment on a $750,000 mortgage at 6.2% for 15 years?

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Multiple Choice

What is the annual payment on a $750,000 mortgage at 6.2% for 15 years?

To determine the annual payment on a mortgage, we use the formula for an annuity, which is applicable when calculating fixed payments over a set period with a fixed interest rate. The formula for the annual payment (A) can be expressed as: \[ A = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1} \] Where: - P is the principal amount (loan amount), - r is the annual interest rate (expressed as a decimal), - n is the total number of payments (number of years in this case, since payments are annual). In this situation: - P = $750,000 - r = 6.2% = 0.062 - n = 15 years Plugging these values into the formula, we first need to calculate: 1. \( (1 + r)^n \): \[ (1 + 0.062)^{15} \approx (1.062)^{15} \approx 2.4583 \] 2. Then, calculate the numerator: \[ P \times r \times (1 + r)^n = 750,000 \times 0

To determine the annual payment on a mortgage, we use the formula for an annuity, which is applicable when calculating fixed payments over a set period with a fixed interest rate. The formula for the annual payment (A) can be expressed as:

[ A = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1} ]

Where:

  • P is the principal amount (loan amount),

  • r is the annual interest rate (expressed as a decimal),

  • n is the total number of payments (number of years in this case, since payments are annual).

In this situation:

  • P = $750,000

  • r = 6.2% = 0.062

  • n = 15 years

Plugging these values into the formula, we first need to calculate:

  1. ( (1 + r)^n ):

[ (1 + 0.062)^{15} \approx (1.062)^{15} \approx 2.4583 ]

  1. Then, calculate the numerator:

[ P \times r \times (1 + r)^n = 750,000 \times 0

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