Career Development

How to Calculate APR

February 22, 2021

Borrowing funds from an institution or lending money has an associated cost. Banks and financial institutions make money from the deposits that people put in their care. They make a profit by charging people who borrow from them a certain percentage of the borrowed money. In this article, we explain what APR is, the types of APR and how to calculate it.

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What is APR?

Annual percentage rate, or APR, is the total cost of borrowing from a financial institution over one year. Annual percentage rate is a good way to calculate the cost of borrowing because it takes into account all associated costs of borrowing, including extra charges like late fees, closing fees and administrative fees.

APR does not take into account the compounding effect of interest where it applies. APR is used to compare costs across different lenders.

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Types of APR

There are two types of APR:

  • Fixed APR: In a fixed APR, the interest rate applied to the principal amount borrowed does not change. The APR calculated based on the interest rate will also be fixed. There is no variation of the rate, and so the amount paid per year for borrowing that money remains the same.
  • Variable APR: A variable APR is subject to change because the interest rate applied to the principal varies from time to time. It depends on the movement of the U.S. prime lending rate. The variable nature means that once there is an upward surge in interest rate, the borrower pays more.

The higher the APR is, the more interest is paid by the borrower. Credit card holders who pay their bills in full and on time tend not to be affected by APR. This is because APR is calculated based on the remaining balance. If the balance is paid out in full and on time, the APR will not apply.

How to calculate APR

To calculate the APR of a loan, you need to take into consideration the principal amount, the number of years the loan will last and the extra charges that the loan incurs in addition to interest.

To calculate APR, use the following steps:

  1. Calculate the interest rate
  2. Add the administrative fees to the interest amount
  3. Divide by loan amount (principal)
  4. Divide by the total number of days in the loan term
  5. Multiply all by 365 (one year)
  6. Multiply by 100 to convert to a percentage

Here is the annual percentage rate formula:

APR = ((Interest + Fees / Loan amount) / Number of days in loan term)) x 365 x 100

For example, Frances borrows $2,000 at a 5% interest rate for two years. The closing administrative cost for the loan is $200. To find the APR, first calculate the Interest on this loan using the simple interest formula: A = (P(1+RT), where A = total accrued amount, P = principal, R = interest rate and T = time period.

In this case, P = $2000, R = 5% and T = 2 years. Therefore, A = ( 2000(1+0.05x2)), or A = $2,200.

Interest accrued = A - P = $2200 - $2000 and interest = $200.

Next, add the interest to the closing cost. Using the APR formula, fees + interest = $200 + $200 = $400.

Finally, divide the loan amount and the number of periods, then multiply by 100 to get a percentage.

APR = (400/2000) / 2 x 1 x 100 = 10%

The APR on this loan is 10%.

From the APR calculations, you can discover that even though it appears that the interest rate is 5% on this loan, the real annual cost of this loan is 10% when all the charges are included.

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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%.

APR vs. nominal interest rate

Nominal interest rate is the rate of interest without taking account of inflation. It is not the real interest rate as used by banking institutions. Nominal interest rate when adjusted for inflation becomes the real interest rate, which is usually different from the nominal interest rate.

When banks advertise their interest rates, it is usually the nominal rates that are advertised. Nominal rates are the base rates that banks use for lending.

When depositors make a deposit or an investment with a bank, they expect to make money on their investment. The amount earned is determined by the real interest rate, not the nominal interest rate.

The real interest rate can increase or decrease. When there is an increase, the depositor makes more money, and if the real rates fall, they make less.

Key differences between APR and nominal interest rate

There are a few key differences between APR and nominal interest rate, including the following:

  • Annual percentage rate calculates the total cost of borrowing per year, while nominal interest rate is the interest rate that a borrowed amount attracts.

  • Annual percentage rate makes use of the real interest rate that is adjusted for inflation and also includes other ancillary administrative costs of borrowing per year. The nominal interest rate does not consider inflation.

  • Annual percentage rate is used to compare loans realistically for a borrower, while the nominal interest rate used to compare loans may not be accurate.

Disadvantages of APR

APR, while a good measure for calculating the total cost of borrowing, also has drawbacks that make it imperfect for comparing loans. Below are the key disadvantages of using APR alone as a comparison index when choosing a loan package:

  • APR only works when you know that you will pay the loan in full term. If you plan to refinance the loan halfway through, the terms and conditions for getting a new APR from a different lender may change, making your initial APR calculations useless.

  • APR differs from lender to lender. When shopping for a loan, it is important to check all the rates being offered, especially with the ancillary costs and variable interest rates. If the interest rate is variable, the APR may not be accurate, as any change in interest rate will affect the overall cost of the loan.

  • APR does not take into account the compounding effect of interest rates. Where there is a compounding effect of interest rate in a loan choice, the APR will not be a good indicator of cost.

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