APR Calculator
About This APR Calculator
This APR calculator helps you estimate the Annual Percentage Rate (APR) for various amortizing loans, including personal loans, secured loans, car loans, and home mortgages. The calculator shows the loan cost breakdown and payment amount based on your input.
To use this APR calculator, enter your loan information, which includes the loan amount, interest rate, and loan term. You should also input any upfront and loaned fees the lender charges and adjust payment and compounding frequencies.
Once you have adjusted the inputs, you should be able to see your APR and other loan information in the results section. You can see the loan breakdown into the initial loan, interest cost, upfront fees, and loaned fees. You can also find the complete payment schedule below.
What Is APR
APR (Annual Percentage Rate) is the total cost of borrowing, including interest charges and any other fees, expressed as an annual percentage. The main difference between APR and interest rates is that APR accounts for the fees a lender may charge. These fees may include upfront charges and loaned charges. If there are no lender fees, the APR equals the interest rate, but if there are any lender fees present, the APR will be larger than the interest rate.
How to Calculate APR
There are different ways to calculate APR. The simple way is to sum up all loan costs, divide by the loan amount, and adjust the loan length to 1 year. This method can be useful for short-term loans of about 1 year. A more complex method allows you to calculate the APR even over large time frames, such as car loans and mortgages.
Simple Way How to Calculate APR
A simplified APR calculation allows you to easily estimate your APR on short-term loans. This formula may be inaccurate for loans with a maturity longer than 1 year. It requires two ratios: cost ratio and annualization factor.
This ratio represents the total cost of the loan relative to the loan amount. It is the % of the loan you have paid in fees and interest.
This factor adjusts the term length to a single year. The annualization factor should be less or equal to 1. If it is larger than 1, the final result is not accurate.
Precise Way How to Calculate APR
Actuarial method for calculating APR is precise for all loan terms, but it is more complex to calculate than the simplified method. The following steps can help you calculate APR on your loan.
| Variable | Definition |
|---|---|
| PV | Loan Principal |
| r | Interest Rate |
| n | Loan Term |
| k | Compounding Frequency |
- Calculate Monthly Payment: Calculate how much you will have to pay for your loan periodically. Make sure to include any loaned fees to the principal for accurate measurements. You can use the following formula to calculate your periodic payment.
- Estimate Net Loan Amount: If you have upfront fees, then you should subtract it from your loan amount. For example, if your loan is $10,000 and you pay $1,000 in origination fees, your net loan amount is only $9,000.
- Find the APR: You need to find the interest rate using the payment and the net loan amount found above. The loan period should stay the same. You need to estimate the interest rate that would yield a balance of $0.00 at the end of the loan term. There is no formula to compute it. You can use a formula RATE in excel or google sheets to find the APR.
Example of an APR Calculation
Simplified APR Calculation
Let’s say you took out a $10,000 personal loan with an interest rate of 5% for 1 year that is payable in full at the end of the year. The bank charged you a $1000 origination fee where $500 are paid upfront and the other $500 are added to the loan.
- Find Your Periodic Payment Amount
- Calculate Total Interest Paid
- Calculate Cost Ratio
- Calculate Annualization Factor
- Calculate the APR
Actuarial APR Calculation
Let’s go over the same example to see what APR will actuarial method yield.
- Find Your Periodic Payment Amount
- Find Net Loan Amount
- Find an APR
This should be done iteratively by increasing interest rate with small increments until the final balance is minimized. Increment size determines the precision of the estimation. Final balance should increase as the interest rate increases. Once your final balance is as close to 0 without turning positive is your best APR estimation.
Compounding Interest in APR
APR does not take into account the compounding of interest. If you are concerned about the effect of compounding interest, you can use annual percentage yield (APY). While APY takes the effects of compounding into consideration, it does not take into account other fees and charges.
APR is often the best metric for comparing different credit products. In the case of fixed-income investments, investors often reinvest their interest earnings. Thus compounding of interest becomes more prominent. Also, for most savings accounts and GICs, there is no fee. Therefore, APY is the appropriate measure for comparing these investments.
APR Costs
APR includes some costs but does not account for other costs. Understanding what APR includes is important to avoid financial surprises down the road. This section will examine what is and isn’t included in the APR.
What’s Included
Most personal loans, lines of credit, and car loans have fees associated with them. These fees are accounted for in the APR calculation because they are direct costs of the loans. The following fees can be included in APR.
- Legal Fees
- Mortgage Broker Fees
- A Home Appraisal Fee and
- Home Inspection Fees if required
- An Origination Fee
- Other Fees for Special Loans (i.e. Student Loans)
What’s Not Included
Charges and fees to exclude from the APR calculation:
- Mortgage Prepayment Penalties
- Optional Legal Fees for services not required by the lending bank
- Home inspection fees if not required by the lending bank
- Title Insurance
- Mortgage Default Insurance (such as CMHC Insurance premiums)
Why Use APR?
APR is used because it reflects your true cost of borrowing. Canada’s Bank Act requires banks to disclose the cost of borrowing when a borrower is applying for credit. This ensures that borrowers are informed about how much it will cost them and APR calculation allows you to compare the costs of one loan with other loans.
Examples of APR
Example 1: Payday Loans
Cash 4 You is a payday lender that offers payday loans in Ontario. Ontario’s Payday Loans Act regulates the maximum cost of borrowing for payday loans. Cash 4 You charges $15 for every $100 borrowed. While most payday loans must be paid back in 2-4 weeks, the maximum allowed term in Ontario is 62 days.
If you borrowed $100 for 62 days, your APR would be 88.3%.
Example 2: Credit Card Balance Transfer Offers
Many credit cards in Canada offer promotional or introductory rates for new applicants. The Tangerine Money-Back Credit Card offers a balance transfer promotional offer rate of 1.95% for 6 months, with a 1% balance transfer fee.
If you transferred over and borrowed $1,000 during the promotional period only, you would be charged an initial balance transfer fee of $10. The promo rate of 1.95% is stated as an annual rate.
To simplify, assume that only interest payments are made. The APR including the balance transfer fee would be 3.95%.
Example 3: Effects of Time on a Mortgage APR
The longer the term of your loan, the more time there is for your fixed costs to be spread out over. For example, a home appraisal would cost the same whether you are looking to get a mortgage with a one-year term or a five-year term.
Private mortgages have short-term lengths and private mortgage lenders often charge significant fees. To see how APR is affected by the duration of your loan, let’s look at a six-month private mortgage and a two-year private mortgage. If there are the same fees charged, such as lender fees, broker fees, and appraisal fees, then the six-month mortgage will have a higher mortgage APR compared to the two-year mortgage.
If a homeowner wanted to borrow for two years with six-month terms, they would need to renew their six-month mortgages three more times. Some private lenders may charge a renewal fee that is lower than initial lending fees, while others may charge fees just as they would for a new mortgage. In comparison, the homeowner could have paid them just once with a two-year mortgage.