Economist specializing in debt market transparency and consumer credit regulation.
The **Annual Percentage Rate (APR) Calculator** helps you quickly solve for the missing element in a simple interest loan, including the total interest/fees, the principal amount, the loan term in days, or the APR itself. Enter any three known variables to determine the fourth.
Annual Percentage Rate Calculator
Annual Percentage Rate Formula Variations
The calculation is based on the simple interest approximation, adjusted to an annual rate over a period in days (365 days in a year).
Let $I$ = Total Interest/Fees, $P$ = Principal, $D$ = Term in Days, and $APR$ = Annual Percentage Rate.
Formula Source: Investopedia – APR Definition
Solving for each variable:
APR (Q) = [ (I ÷ P) × (365 ÷ D) ] × 100
I (F) = (APR × P × D) ÷ 36500
P (P) = (I × 36500) ÷ (APR × D)
D (V) = (I × 36500) ÷ (APR × P)
Variables Explained
- F (Total Interest & Fees): The total monetary cost of the loan (interest plus any mandatory fees).
- P (Principal Loan Amount): The initial amount of money borrowed.
- V (Loan Term in Days): The total duration of the loan, measured in days.
- Q (Annual Percentage Rate %): The annualized cost of the loan, including all fees, expressed as a percentage.
Related Calculators
- Effective Annual Rate (EAR) Calculator
- Simple Interest Loan Calculator
- Nominal Interest Rate Calculator
- Debt Comparison Calculator
What is the Annual Percentage Rate (APR)?
The **Annual Percentage Rate (APR)** represents the true annual cost of borrowing money. Unlike the nominal interest rate, the APR includes not only the basic interest charge but also any additional fees or costs associated with obtaining the loan, such as origination fees or points. Because it standardizes the total cost across a yearly basis, the APR is the most effective metric for comparing different loan offers from various lenders.
While the APR provides an annualized cost, it often assumes simple interest and does not account for compounding frequency (which is captured by the Effective Annual Rate or EAR). However, U.S. Truth in Lending Act regulations require lenders to disclose the APR so consumers can make informed decisions about credit products.
How to Calculate APR (Example)
Let’s solve for the APR (Q) given the other three inputs:
- Gather Variables:
Total Interest & Fees (F) = $500
Principal Loan Amount (P) = $5,000
Loan Term (D) = 365 days (1 year)
- Calculate Interest Rate (Daily):
$$(\$500 \div \$5,000) \times (365 \div 365) = 0.10 \times 1 = 0.10$$
- Convert to Annual Percentage Rate:
$$\text{APR} = 0.10 \times 100 = 10.0\%$$
- Final Result:
The Annual Percentage Rate is 10.0%.
Frequently Asked Questions (FAQ)
The interest rate is just the cost of borrowing principal. The APR includes the interest rate *plus* mandatory fees (like closing costs, discount points, etc.) to give you the total annual cost.
Why is APR based on days (365)?APR is annualized to provide a standard rate of comparison. Using days ensures an accurate conversion of short-term interest charges (like those from payday loans or short-term installment loans) into a comparable annual rate.
Does compounding affect simple APR?This simple APR formula does not account for compounding. If a loan compounds interest, the actual rate paid (the Effective Annual Rate, or EAR) will be slightly higher than the stated APR.
Is a low APR always better?Generally, yes. A lower APR means a lower overall cost for the loan. However, you should also consider other factors like variable vs. fixed rates, prepayment penalties, and total loan term.