APR Calculator
APR is evaluated from Loan Amount, Stated Interest Rate and Loan Term. The calculation reports Monthly Payment, True APR and Rate vs APR Spread.
Results
About the APR Calculator
The APR calculator is a valuable tool for anyone considering a loan, as it helps borrowers understand the true cost of borrowing. By taking into account the loan amount, stated interest rate, loan term, and total fees, the calculator provides a clear picture of the monthly payment, true APR, and the difference between the stated rate and the true APR. This information is essential for making informed decisions when comparing loan offers or evaluating the impact of fees on the total cost of a loan. For instance, a borrower may think they are getting a good deal with a low stated interest rate, but the APR calculator can reveal that the fees associated with the loan actually increase the true APR, making the loan more expensive than initially thought.
### History of the APR Calculator
The concept of APR, or Annual Percentage Rate, has its roots in the Truth in Lending Act (TILA) of 1968 in the United States. This act required lenders to disclose the terms of a loan, including the APR, to borrowers. The APR was designed to provide a standardized measure of the cost of credit, allowing borrowers to compare different loan offers on an equal basis. Over time, the calculation of APR has evolved to take into account various fees and charges associated with loans. The APR calculator, as a tool, has become increasingly sophisticated, incorporating complex formulas and algorithms to provide accurate calculations. The development of online APR calculators has made it easier for borrowers to access this information and make informed decisions about their loans.
### The Science Behind the Calculations
The APR calculator uses a formula that takes into account the loan amount, stated interest rate, loan term, and total fees. The formula for calculating the monthly payment is: M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1], where M is the monthly payment, P is the loan amount, i is the monthly interest rate, and n is the number of payments. The true APR is calculated using the formula: APR = (1 + i)^12 - 1, where i is the monthly interest rate. The rate vs APR spread is calculated by subtracting the stated interest rate from the true APR. These formulas require the input of several variables, including the loan amount, stated interest rate, loan term, and total fees. The calculator then uses these inputs to calculate the monthly payment, true APR, and rate vs APR spread.
### Real-Life Application and Examples
Consider a borrower who is applying for a $300,000 mortgage with a stated interest rate of 6.75% and a loan term of 30 years (360 months). The lender quotes a total of $6,000 in fees and closing costs. To understand the true cost of the loan, the borrower uses the APR calculator. The calculator requires the borrower to input the loan amount, stated interest rate, loan term, and total fees. Using these inputs, the calculator calculates a monthly payment of $1,945.23, a true APR of 7.12%, and a rate vs APR spread of 0.37%. The borrower can use this information to compare different loan offers and determine which one is the most cost-effective. For example, if another lender offers a mortgage with a stated interest rate of 6.50% but higher fees, the borrower can use the APR calculator to determine which loan has the lower true APR. By using the APR calculator, the borrower can make an informed decision and avoid paying more in interest and fees than necessary.
Formula & How It Works
The calculation applies the following relations exactly as recorded in the metadata: APR is calculated by finding the discount rate that makes the present value of all payments equal to the net proceeds (loan amount minus fees). Net Proceeds = Loan Amount - Fees Monthly Payment = same as standard amortization at stated rate APR = rate (r) such that: Net Proceeds = Payment x [1 - (1+r)^ - n] / r This requires an iterative Newton-Raphson or bisection solve (not a closed-form formula). Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.
Worked Examples
Example 1: Standard Mortgage APR
Inputs
With Loan Amount = 350,000, Stated Interest Rate = 6.75, Loan Term = 360 and Total Fees & Closing Costs = 7,000 as the stated inputs, the result is Monthly Payment = $2,270.09, True APR = 6.948% and Rate vs APR Spread = 0.198%. Each value corresponds to the declared output fields.
Example 2: High-Fee Low-Rate Offer
Inputs
With Loan Amount = 300,000, Stated Interest Rate = 6.25, Loan Term = 360 and Total Fees & Closing Costs = 12,000 as the stated inputs, the result is Monthly Payment = $1,847.15, True APR = 6.641% and Rate vs APR Spread = 0.391%. Each value corresponds to the declared output fields.
Example 3: Short-Term Personal Loan
Inputs
With Loan Amount = 10,000, Stated Interest Rate = 12, Loan Term = 36 and Total Fees & Closing Costs = 400 as the stated inputs, the result is Monthly Payment = $332.14, True APR = 14.863% and Rate vs APR Spread = 2.863%. Each value corresponds to the declared output fields.
Example 4: No Fees — APR Equals Rate
Inputs
With Loan Amount = 25,000, Stated Interest Rate = 9.99, Loan Term = 60 and Total Fees & Closing Costs = 0 as the stated inputs, the result is Monthly Payment = $531.05, True APR = 9.99% and Rate vs APR Spread = 0%. Each value corresponds to the declared output fields.
Common Use Cases
- Find the true APR of a mortgage including all fees
- Compare loan offers on an apples-to-apples APR basis
- Understand how fees affect the effective cost of borrowing