Real APR: 6.335%

Amount Financed  $100,000.00
Upfront Out-of-Pocket Fees  $1,500.00
Payment Every Month  $1,110.21
Total of 120 Payments  $133,224.60
Total Interest  $33,224.60
All Payments and Fees  $134,724.60
View Amortization Table

APR vs. Nominal Interest Rate vs. Daily Periodic Rate

An APR tends to be higher than a loan’s nominal interest rate. That’s because the nominal interest rate doesn’t account for any other expense accrued by the borrower. The nominal rate may be lower on your mortgage if you don’t account for closing costs, insurance, and origination fees. If you end up rolling these into your mortgage, your mortgage balance increases, as does your APR.

The daily periodic rate, on the other hand, is the interest charged on a loan’s balance on a daily basis—the APR divided by 365. Lenders and credit card providers are allowed to represent APR on a monthly basis, though, as long as the full 12-month APR is listed somewhere before the agreement is signed.

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Whats The Difference Between APR Vs. APY?

There’s another important number to consider when taking out a loan or applying for a credit card: the annual percentage yield.

As previously mentioned, APR is a measure of the yearly cost of your loan if your loan is based on simple interest. APY is used in cases where interest is compounded, such as with savings accounts or credit card debt. In the APR calculation example, the borrower paid $120 in interest for a $2,000 loan. That means that they were charged 6% of the principal, calculated once, which would be the simple interest.

In some cases, interest on your loan is compounded, or calculated at a regular interval and then added to the principal owed. When interest is next compounded, it’s calculated using the now higher principal amount. This is how credit cards and adjustable-rate mortgages work. APY represents the annual cost of your credit card or loan while also factoring in how often interest is applied to the balance you owe on the card or loan.

How to manage your credit card interest

Calculating your credit card interest is just the first step. By monitoring your APR and by aiming to pay off your balance as much as you can, you can pay much less in interest and improve your credit score at the same time. Of course, if you pay your balance in full within the specified grace period every month, you won’t have to pay any interest on purchases. You may still be charged interest for other types of transactions; like when you use your card to get cash.

Keep your credit card interest at a healthy level by doing the following:

  • Determine whether your credit card APR is fixed or variable.

    This will be indicated on your card statement, often as an (F) or a (V) in the rate table. A fixed rate stays the same from month to month (although card issuers can change the fixed rate with 45 days’ notice or if you are 60 days past due on your minimum payments). The variable rate may change from month to month and is pegged to the prime rate: a reference rate used by many issuers.

  • Reference your statements for your running interest total.

    Your card statements will show how much in interest (and fees) you have accrued year-to-date. Monitoring this figure helps you understand how much you’re paying in credit card interest, without having to do the manual calculations described above.

  • Aim to pay your statement balance in full each month.

    Put your credit card to work as a short-term interest-free loan by paying off what you owe at the end of each statement cycle. You will likely have a minimum of 21 days from the date the statement is mailed to pay off the balance before interest begins to accrue. If you want to pay your statement balance in full each month, you may want to consider signing up for that option through autopay, so that you won’t forget to make a payment.

  • But when you can’t pay in full, always try to pay more than the minimum balance due.

    Your card statement or online account will detail the minimum amount due for each statement cycle. The more of your balance you pay each month, the less you will owe in interest.

APR on Loans Explained

The APR on a loan – a mortgage, for example – marks the total yearly cost associated with borrowing money from a financial institution.

Since more fees beyond just interest expenses are considered in the APR of a loan, the metric provides a more accurate estimation of how much in total that a borrower must pay to take out a loan.

The APR on loans facilitate comparisons across different loan offerings (i.e. for the borrower to pick the cheapest option), yet in actuality, the comparison is not “apples-to-apples” due to several factors:

  • Oftentimes, loans tranches can be “taken out” (i.e. repaid in full earlier than scheduled) or refinanced before the date of maturity.
  • Standardizing the fees charged by the lender is practically impossible (i.e. different types per financing arrangement).
  • Contingencies can be influential factors such as prepayment penalties, conditional fees, and incentive programs.
Credit Card APR

Under the context of credit cards, the APR determines the amount of interest due based on the carrying balance from month to month.

If each monthly bill is paid in full and on time, no interest will be incurred.

Unique to credit cards, interest is calculated daily, meaning that a credit card company charges borrowers by multiplying the ending balance by the APR and then dividing by 365.

The amount of interest charged is subsequently added to the outstanding balance the following day.

In contrast to credit cards, the APR on a loan reflects more than just the interest payments that must be met.

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Why Do Credit Cards Have Different APRs?

You might notice that your credit card has an APR range that shows more than one APR in the fee disclosures or your credit card statement. Credit card companies often charge a variable APR, according to the type of transaction.

The most common credit card APR categories apply to:

  • Balance transfers — usually at a lower fixed rate for a limited time
  • Cash advances — often higher and more expensive than the standard APR
  • Introductory — usually available for a limited time after sign-up
  • Penalty or late payment — often more expensive than the standard APR
  • Standard purchases — the main APR for store and online purchases

How To Calculate APR on a Loan

To calculate APR, follow these steps:

  1. Add up all interest charges and divide by the amount you borrowed or currently owe.
  2. Multiply by 365
  3. Divide by the number of days left in the loan

For example: Finding the APR of a short-term loan of $500 with $60 in total fees and interest and a 14-day term:

  1. $60 ÷ $500 = 0.12
  2. 0.12 x 365 = 43.8
  3. 43.8 ÷ 14 = 3.1286% APR

How To Calculate APR on a Credit Card

Calculating APR on credit card is different than the method for other loan products. Credit card APRs change as the interest rates and prime rate set by the banks change. A bank or credit card issuer isn’t legally obligated to notify you, so it’s important to monitor for changes.

To find a credit card’s APR, add the current U.S. bank prime loan rate and the interest rate the credit card issuer charges. For example, the U.S. prime rate is currently 5%. If the card provider’s credit card interest rate is 4%, the consumer credit card rate will be 9% APR — 5% prime rate + 4% card interest rate = 9% APR.

 

How To Calculate APR on a Car Loan

Here’s how to calculate APR for a car loan in four steps:

  1. Get the total payment amount by multiplying the monthly payment by the term of the loan in months.
  2. Subtract the amount borrowed from the total payment amount to find the loan’s total interest payments.
  3. Divide the total interest charges by the number of years on the loan to find the yearly interest amount.
  4. Divide the yearly interest amount by the total payments to calculate APR.

For example: To calculate APR on a $16,000 vehicle loan for five years (60 months) with a $400 per month payment:

  1. $400 x 60 = $24,000 (total payment amount)
  2. $24,000 – $16,000 = $8,000 (interest fees)
  3. $8,000 ÷ 5 = $1,600 (yearly interest amount)
  4. $1,600 ÷ $24,000 = 0.0667% APR

How To Calculate APR on a Mortgage Loan

Manually calculating the APR on a mortgage loan is tricky. Luckily, mortgage lenders are required by law to provide an APR to borrowers, so you can skip the hard work. Alternatively, keep reading to learn how to calculate APR on a mortgage using a spreadsheet.

Amortization

With many loans, your loan balance changes every month. For example, on auto, home, and personal loans, you gradually pay down your balance over time, and you usually end up with a lower balance each month.

That process is called amortization, and an amortization table helps you calculate (and shows you) exactly how much interest you pay every month.

Over time, your monthly interest costs decrease—and the amount that goes toward your loan balance increases.

Using the APR calculator – Variables and financial terms

Now that you have some information on the background of different type of interest rates from the previous section, it is time to get familiar with our APR calculator so you can analyze a loan construction from multiple angles to ensure you incorporate all emerging financial costs.

As a starting point, let’s go through the parameters and terms you may encounter on this page. To be consistent, we have grouped the variables according to their roles: first are the ones that you need to provide in order to specify the loan construction (input variables), followed by the ones that result from these previously stated parameters and provide a base for the evaluation or comparison of the particular loans (output variables). Lastly, you can check out the supplementary variables that are the by-product of the computational process, which can be found in the advanced mode.

  1. Loan Specification

To make this calculator work, you need to provide the following values:

  • Loan amount (A) – the amount of loan under consideration.

  • Interest rate (r) – the annual nominal interest rate as a percentage. Note that percentage rates are generally converted to decimals for complex computations (for example 6% = 0.06).

  • Loan term (t) – the interval over which you need to repay the Loan Amount and all connected cost (interest and other additional fees).

  • Compounding frequency (m) – the number of times interest compounding occurs. For example, when compounding is applied annually, m=1, when quarterly, m=4, monthly, m=12, etc.

  • Payment frequency (q) – the regularity that part of the loan is repaid.

  • Fees rolled into loan – all additional fees that are paid during the loan term. Since it is attached to the loan amount, banks generally charge interest on it.

  • Fees paid separately – fees that are payable in advance (Prepaid Finance Charge) or at the time the loan is consummated. Interest is not charged on these fees, but it still raises the APR of a loan.

  1. Main Results

The main and additional results are the immediate output of the previously specified loan construction section:

  • Effective Annual Rate (EAR) – an estimate of the yearly rate adjusted by the compounding effect. As it was mentioned, this indicator doesn’t account for any additional costs attached to the loan.

  • Annual Percentage Rate (APR) – estimates the cost of borrowing per year as a percentage of the Loan Amount. It takes into consideration all additional costs without incorporating the compounding factor.

  • Effective Annual Percentage Rate (Effective APR) – the APR adjusted by the effect of compounding – the ultimate indicator for the cost of borrowing in the context of this calculator.

  1. Additional Results
  • Total additional fees – the sum of all costs connected to the loan (Fees rolled into loan plus fees paid separately).

  • Installment or Payment amount (PMT) – the amount of money that needs to be paid over each payment period set by the Payment frequency.

  • Total finance charge or Cost of borrowing – the total expenses of the loan. In other words, this is the total amount of money you pay to use the credit (Interest plus all additional fees).

  • Total Payments – the sum of the Loan amount and Total finance charge; thus, this is the sum of money you need to pay back after signing the loan contract.

  • Total Interest Payment – the sum of interest that comes from borrowing.

  • Principal or Present Value (PV) – the total amount of loan including the rolled in fees (Loan amount plus fees rolled into loan).

  1. Supplementary Information

If you would like to learn more about this topic and how to compute these calculation, the following values can be found in advanced mode:

  • Number of periods (t) – the life span of the loan in years converted from the previously given loan term.

  • Equivalent interest rate (eq_r) and Periodic equivalent interest rate (eq_i) – that interest rates that are computed when the payments and compounding occur with a different frequency. In other words, the equivalent rate is aimed at converting the nominal interest rate from one compounding frequency to another while keeping the Effective Rate unchanged.

For example, assume you have a loan with annual rate of 6 percent (r=6), and you have to pay it back quarterly (q=4), but compounding occurs monthly (m=12). As the payment frequency is quarterly, the interest will be charged on your loan on quarterly bases as well. Hence, to determine the nominal interest rate of a loan paid once a quarter but compounding monthly, you need to find the equivalent interest rate.

The general formula of the equivalent rate and its periodic form are the following.

eq_r = (q * ((1 + r / m) ^ (m / q) - 1))

eq_i = eq_r / q

After substituting the values from our example, we need to solve the following equation:

eq_r = (4 * ((1 + 0.06 / 12) ^ (12 / 4) - 1)) = 0.0603005 ≈ 6.03%

eq_i = 6.03% / 4 = 1.5075%

Note, that the equivalent interest rate only harmonizes the payments and compounding of different frequencies, thus, except the case of annual payment frequency, it is not equal to the Effective Annual Rate (EAR).

  • Approximate APR is a proxy for the Annual Percentage Rate.

Since estimating APR involves complex mathematics, we’ve decided to present to you a simplified formula that gives you an approximate value for the APR:

Approximate APR = (2 * q * Total Finance Charge) / (Loan Amount * (n + 1))

APR vs. APY

While APR gives you the real cost of a loan annually, it does not take into consideration the compounding effect of a loan when the loan is not calculated based on simple interest as seen above.

The calculation of interest payment above is based on a simple interest model that is not widely used for long-term loans like student loans or mortgage loans.

To take into consideration the compounding effect of an interest in a loan, you can use the annual percentage yield (APY) instead of APR.

Annual percentage yield is the amount that is earned from a savings deposit, taking into account the compounding nature of compound interest. Annual percentage yield gives the total amount that savings or investments will yield over a period.

When compared with the annual percentage rate, the annual yield measures what the lender will gain by investing their money, taking into account the number of times that the investment was compounded.

The formula for calculating annual percentage yield is APY = 100[(1+ interest/principal) ^ (365/days in loan term)-1]

For example, Frances received interest of $40 for depositing $2000 in the bank. To calculate the APY for the amount deposited, use the APY formula:

APY = 100[(1+40/2000)^(365/365)-1]

The annual percentage yield is 2%.

Fixed APR vs Variable APR

The final difference we’ll explain is between a fixed APR and a variable APR:

  • Fixed APR: APR remains unchanged throughout the borrowing period.
  • Variable APR: APR fluctuates due to being tied to a prime rate.

A fixed APR is thus more predictable than a variable APR, which is a function of the market conditions and the specific benchmark by which its value is influenced.

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