You enter the nominal rate of interest and the compounding period, which can be yearly, half-yearly, quarterly, monthly, semimonthly, bi-weekly or weekly. The calculator presents you with the Annual Percentage Yield (APY). Alternatively, if you know the APY and the compounding period, you can enter them, and our calculator will produce the nominal interest rate.
Further, by entering an initial investment amount and term, the calculator will use the interest rate you entered in the previous step and calculate the final balance. Alternatively, you can enter the final balance, and the calculator will calculate the initial investment amount.
APY stands for Annual Percentage Yield, otherwise called effective annual rate (EAR). APY represents the annual rate of return on investment, considering the effects of compounding. In other words, APY measures the total interest or return an investment earns in a year, expressed as a percentage of the initial investment.
APY considers that, in a compounding investment, the interest earned is added to the principal amount, and the new total becomes the basis for future interest calculations. As a result, the effective yield of the investment grows over time.
For example, if you invest $1,000 in a savings account that pays 4% interest compounded monthly, at the end of the first month, you would have $1,003.33 (the original $1,000 plus $3.33 in interest). If you leave the money in the account for another month, the interest earned in the first month would be added to the principal, and you would earn interest on the new total of $1,003.33. Thus the second month’s interest would be $3.34. The APY considers this compounding effect and calculates the total rate of return over the entire year. In this example, the final balance would be $1040.74, and the APY is 4.074%.
r: nominal rate of interest
n: number of compounding periods in each year
APY or effective annual rate (EAR) is often used for comparing different fixed income investments. This is because compounding frequency is usually the important factor distinguishing different investment products with close nominal interest rates.
Lending products with comparable nominal interest rates often differ in terms of the fees they charge. So to compare loans, we need to define a metric that includes both the interest rate and the fees charged for the loan. This metric is called the Annual Percentage Rate (APR).
APR is the rate of interest which results in your total interest cost (all the interest you would pay over the term of the loan using APR) becoming equal to the total of your current interest cost and loan fees (all the interest you would pay over the term of the loan using stated interest rate + all fees and charges associated with the loan). You can use WOWA's APR calculator to compare different loans.
We can roughly summarize this section by stating that: APY is for interest that you earn, while APR is for interest/fees that you pay.
As we mentioned, when you are borrowing, you often have to make periodic payments which prevent interest from being compounded. Yet, if we examine the effect of compounding in more detail, we can see that compounding would benefit a borrower if they make their payments more frequently than the interest is compounded. While compounding can cost borrowers if they make their payments less frequently than the interest is compounded on their loan.
As an example, consider Canadian mortgages. The Canadian parliament has legislated that interest on any loan with a fixed rate which is secured by real property (mortgage), should compound half-yearly or less frequently. As a result, most Canadian mortgages are compounded semi-annually.
Thus your mortgage is compounded semi-annually while your payment is monthly (mortgage payments can be semi-monthly, bi-weekly or weekly as well, yet the result of our discussion would not be affected). You are paying interest every month while you were entitled to let the interest accumulate for half a year before paying it.
In order to compensate you for making payments earlier than you are required to make, the bank uses your effective annual rate (EAR) instead of your nominal interest rate in calculating the interest portion of your monthly payment.
For example, if a mortgage has an interest of 5% compounding semi-annually, its EAR (APR) is 5.0625%. An interest rate of 4.949% compounded monthly would have the same EAR of 5.0625%. If you were to make weekly payments, your interest rate would become 4.941%, as this rate with weekly compounding has the same EAR of 5.0625. Thus the compounding effect allows you to pay a lower interest rate when you are making more frequent payments.