Annual percentage rate (APR) and annual percentage yield (APY) are both types of interest rates. Both these terms look similar but are significantly different.
APR is a simple interest rate whereas APY is the yield that considers the compounding effect of interest. This results in significantly different uses for both these rates.
Let us discuss what are APR and APY and their key differences.
What is APR?
The annual percentage rate or APR is the interest rate charged to the loan amount or paid on an investment.
APR can be calculated on a daily, monthly, semiannually, or annually basis depending on the loan or investment terms. It is commonly referred to as the interest rate charged to loans and debt products.
APR is the interest rate charged to the principal loan amount plus the originating fee, commission, or any other charges included by the lender. Often, mortgage agreements include the loan originating fee with the principal amount as well.
How Does APR Work?
APR does not account for the compounding effect. However, if it is expressed in a periodic term, it is converted into an annual rate.
APR is calculated by multiplying the periodic interest rate by the number of periods. In other words, a simple interest rate is converted into an annualized rate.
The formula to calculate APR is:
APR = Periodic Rate x Number of Periods in a Year
The periodic monthly payment includes a portion of the interest rate and the principal loan amount. As the loan progresses, the interest proportion of the loan payment increases and the principal proportion decreases.
When comparing different APRs, borrowers must consider the payment frequency. Although APR does not account for compounding, the effective interest rate will change depending on the payment frequency.
For example, a 7% APR charged annually with a payment frequency of once yearly will be lower than for the same rate but a monthly payment schedule which effectively translates into a 7.23% rate.
Similarly, lenders will use the lowest APRs for loan products. However, banks must disclose the payment frequency and loan terms clearly to the borrowers.
Fixed and Variable APRs
Banks charge two types of annual percentage rates on loans and credit cards. A fixed APR and a variable APR.
A fixed-rate does not change over the loan term. Borrowers are guaranteed the same interest rate throughout the loan term irrespective of the market interest rate.
However, banks and lenders will decide on the fixed APR depending on several factors including the borrower’s credit score, creditworthiness, and market interest rate.
Fixed APRs are commonly charged to commercial loans, mortgages, and personal loans with long-term maturities.
On the other hand, the variable interest rate may change over the loan term. It is commonly affiliated with credit cards, line of credit loans, overdrafts, etc.
Variable APRs follow the prime interest rate or the FED interest rate. As these rates change, variable interest rates adjust accordingly.
Example
Suppose a borrower applies for a loan of $30,000 with ABC bank. The loan comes with an APR of 5% and a maturity period of 5 years.
The total interest payable by the borrower will be $ 3,968 over the course of five years. Therefore, the total payable amount by the borrower is $ 33,968.
It translates to a monthly loan installment of $ 566.14 ($33,968/60). The interest proportion of the monthly payment for the first payment will be $125 and the principal proportion will be $441.14.
As the loan progresses, the principal proportion will reduce and the interest proportion will increase. However, the monthly payment will remain fixed at $566.14.
Pros and Cons of Using APR
APR is a widely used term that borrowers can understand easily. It considers only the simple interest rate and does not account for compounding.
It means if the APR is listed, the borrower will have to check the payment frequency and multiply it with the listed rate to calculate the APR.
The drawback of APR is the calculation method is not readily available for loan amortization. Also, lenders may include commission and other charges that would increase the interest payment.
Therefore, borrowers must compare APRs carefully and consider different charges included in the loan amount.
What is APY?
Annual percentage yield (APY) is the interest rate that considers compounding or the time value of the money concept.
It adds periodic interest into the principal amount. Thus, the remaining balance of a loan or the principal amount of investment keeps changing.
The term APY is usually linked to the yield an investor receives from a fixed-income investment like a bond or certificate of deposit.
Compounding interest is the key concept when understanding APY. Also, the compounding frequency of the interest rate will determine the annual yield.
How Does APY Work?
Let us begin with the formula to calculate APY and then explain its working mechanism.
APY = (1+r/n) n – 1
Here “r” is the periodic interest rate and “n” is the frequency or number of payments in a year.
So, APY is the yield or rate of return that you’ll receive on an investment. When you consider the time value of money, APY gives the correct interest amount earned on an investment.
The rate of return on investment can simply be calculated by compounding the interest rate for the given period. However, a standardized form of calculating the rate of return for an investment is APY which converts the total return into an annualized return.
This concept is practically useful when comparing two or more investments with similar rates of returns but different periodic payment schedules.
For example, if an investment has a rate of return of 12% and pays interest annually looks the same as the other investment 1% paying monthly for one year.
However, when we consider the compounding effect, the APY for the second investment is 12.68%. It is a significant difference when you consider a long-term investment proposal.
Fixed and Variable APYs
Like APR, annual percentage yield can also be fixed or variable. A fixed APY is when the rate of return on an investment does not change until maturity.
A variable APY is when the rate of return changes with a change in the index rate or the federal reserve rate.
However, fixed APY is more common as it is usually associated with fixed-income instruments. Also, investors prefer a fixed rate of return when comparing different investment options rather than varying and inconsistent returns.
Example
Suppose an investor invests $10,000 in a fixed-income instrument (CD) that pays at 0.5% monthly. It means the investor receives 12 payments in a year.
APY = (1+r/n) n – 1
APY = (1+0.5%/12) 12 – 1= 1.005 – 1 = 0.5011%
It is 0.01% higher than the simple interest rate for the same investment. It does not seem significant with a return of $50.11 on an investment of $10,000. It is higher than $50 without compounding.
However, when you consider a significant investment in millions by a corporate investor, it adds up quickly.
Consider the same investment for 5 years. Then,
APY = (1+r/n) n*y – 1
APY = (1+0.5%/12) 12*5 – 1 = 1.025 – 1 = 2.53%
Now the investment gives a total return of $253.09 which is more than the arithmetic sum of the yearly investment calculated earlier due to the compounding effect.
Pros and Cons of Using APY
APY is a better measure of the rate of return on investment as it considers the time value of money and compounds interest.
It gives a realistic rate of return as most investments offer the compounding of periodic interests. It helps compare different investments with similar maturity periods.
APY has some drawbacks as well. It does not account for account opening or investment operating costs. Thus, the effective yield can be different from than stated APY.
It is difficult to decide on a good APY even when you consider compounding. It is usually associated with fixed-income instruments whereas the market interest rate can quickly change making the ideal APY look inaccurate.
APR Vs APY – Key Differences
Let us now summarize some key differences between APR and APY.
APR is commonly used for debt and loan products to express the markup charged on the borrowed amount. APY is commonly used for investment and savings products offered by banks.
Both APR and APY are interest rates expressed in annualized terms. However, both can be expressed with payment frequencies which would affect the annualized rate.
APR does not account for interest compounding. It is a simple interest rate whereas APY considers compounding. APY is the yield rather than simple interest.
As APR is commonly attributed to debt products, it can be fixed or variable depending on the type of loan product offered. APY is usually fixed as it is listed with fixed-income and other savings products.
Both APR and APY are expressed in percentage terms. Both these terms represent annualized interest rates and can be expressed for shorter periods like daily, monthly, and quarterly as well.
