Mortgage APR Calculator

What is a Mortgage APR Calculator?

A Mortgage APR (Annual Percentage Rate) Calculator is a financial tool that helps borrowers understand the true cost of a mortgage loan. Unlike the interest rate, which only accounts for the cost of borrowing the principal amount, the APR includes additional costs such as closing fees, points, and other charges associated with obtaining the loan. This calculator provides a more comprehensive view of the loan's cost, allowing borrowers to make more informed decisions when comparing different mortgage offers.

Formula for Mortgage APR Calculation

The APR calculation involves several steps:

1. Calculate the monthly payment using the loan amount, interest rate, and term:
\[P = L \frac{r(1+r)^n}{(1+r)^n-1}\]
2. Calculate the total cost of the loan by adding all monthly payments and closing costs:
\[T = (P \times n) + C\]
3. Calculate the APR:
\[APR = \left(\left(\frac{T}{L}\right)^{\frac{1}{Y}} - 1\right) \times 100\]

Where:

• P = Monthly Payment
• L = Loan Amount
• r = Monthly Interest Rate (Annual Rate / 12)
• n = Total Number of Payments (Years × 12)
• T = Total Cost of the Loan
• C = Closing Costs
• Y = Loan Term in Years

Calculation Steps

1. Convert the annual interest rate to a monthly rate.
2. Calculate the monthly payment using the formula above.
3. Determine the total cost of the loan by multiplying the monthly payment by the number of payments and adding closing costs.
4. Use the APR formula to calculate the annual percentage rate.

Example

Let's consider a scenario with the following details:

• Loan Amount: $200,000
• Interest Rate: 4% per year
• Loan Term: 30 years
• Closing Costs: $3,000

Calculation:

1. Monthly interest rate: 4% / 12 = 0.3333%
2. Monthly payment: $954.83 (using the formula)
3. Total cost: ($954.83 × 360) + $3,000 = $346,738.80
4. APR: 4.154% (using the APR formula)

In this example, the APR (4.154%) is higher than the interest rate (4%) due to the inclusion of closing costs. This difference represents the true cost of borrowing and allows for a more accurate comparison between different loan offers.