Long-term financing, such as auto loans or home mortgages, provides many individuals across the country with the resources they need to finance critical purchases. In many situations, this borrowing platform can be life-changing. That being said, it is important to assess the impact that interest will have on the overall sum of money owed. Depending upon how interest compounds on your loan, you can use a few simple calculations to convert monthly interest rates to annual percentages and vice versa.
Your method for converting a monthly interest rate to an annual interest rate will depend largely on how interest compounds on your loan. The process of conversion is significantly more streamlined if interest compounds annually rather than monthly.
The Basics of Interest Compounding
When you take out a mortgage or any other form of long-term borrowing, you are assigned an interest rate for your loan. This percentage value represents a specific portion of your loan that will be added back onto your principal balance as a form of "premium" for the privilege of borrowing.
When interest is attached to a loan, specific details will also be included relating to how interest compounds, or accrues on top of the principal balance. Generally speaking, interest will either accrue on a monthly or yearly basis. If, for example, your loan has compounding monthly interest, the specific amount of interest apportioned for each month of borrowing will be added back on top of the principal before the next month's balance is calculated.
This differs significantly from annual compounding, in which interest is calculated as a lump sum based on the current annual balance. So, for example, if a $200,000 loan had a 5 percent interest rate that compounded annually, a total of $10,000 would be added back on to the balance at the end of the year.
How to Convert Monthly Interest to APR
Based on this information, you can determine for yourself that calculating monthly interest rates on annually compounding interest is significantly easier than loans where interest compounds monthly.
To convert a yearly interest rate for annually compounding loans, you can simply divide the annual interest rate into 12 equal parts. So, for example, if you had a loan with a 12 percent interest rate attached to it, you can simply divide 12 percent by 12, or the decimal formatted 0.12 by 12, in order to determine that 1 percent interest is essentially being added on a monthly basis. You can simply inverse this process to convert a monthly rate to annual.
That being said, a more complex formula must be used if interest rates are compounded monthly. In order to calculate this, you will first need to convert the monthly interest rate into a decimal-formatted figure. In order to do this, divide the percentage rate by 100. Following this, you will need to add 1 to the figure and then raise this number to the 12th power. Once this is completed, you can subtract 1 from the resulting number and then multiply the figure by 100 to determine the annual interest rate.
Using an Example Calculation
As an example, consider the following: your current monthly interest rate on a loan where interest compounds monthly is a significant 2.5 percent. Divide this figure by 100, which yields the number 0.025. Add 1 to this sum and then raise this to the power of 12. After doing so, you will arrive at the number 1.3448. Subtract 1 from this figure, and then multiply the result by 100. So, your final calculation would be 0.3448 *100 = 34.46. Therefore, your monthly compounding 2.5 percent interest will ultimately become an annual interest rate of 34.46 percent.
- Bankrate: Loan Comparison Calculator
- Compound Interest Calculator | Investor.gov
- Quicken. "What Is a Periodic Interest Rate?" Accessed Jan. 16, 2020.
- Metro Credit Union. "How Loan Amortization Works." Accessed Jan. 16, 2020.
- Consumer Financial Protection Bureau. "What Is the Difference Between a Mortgage Interest Rate and an APR?" Accessed Jan. 16, 2020.
- Discover. "How Does My Credit Card Interest Work?" Accessed Jan. 16, 2020.
- Ally. "APY, APR, and Interest Rates: What You Need to Know and the One Thing You Don’t Want to Overlook." Accessed Jan. 16, 2020.
- Credit card companies use nominal APR compounded monthly, which is different than the effective APR. The conversion of APR to EAR is: (1 + APR divided by 12)^12 - 1*100. So a credit card claiming an APR of 24.99% is actually charging an effective APR of 28.06%. The APR is intended to make loan pricing comparisons easier for borrowers. However, lenders often include other items such as loan origination, service and late fees in the calculation of APRs, making it difficult and confusing to calculate. The APR will differ from the advertised rate, and is often misleading.
Ryan Cockerham is a nationally recognized author specializing in all things innovation, business and creativity. His work has served the business, nonprofit and political community. Ryan's work has been featured at Zacks Investment Research, SFGate Home Guides, Bloomberg, HuffPost and more.