How to Annualize Interest Rates & Calculate Annual Interest

Most investments or loans usually have a rate of interest associated with them. However, these interest rates have different names and implications for your pocket. Time periods can vary.

The amount of interest can be calculated annually or semiannually. Others may follow monthly interest rates, while some may calculate daily interest. This will also depend on the lender or financial institution. There are two basic ways to annualize interest rates: calculating the annual percentage rate (APR) and annual percentage yield (APY).

• The interest rate formula for APR is: ‌APR = Periodic Rate x Number of Periods in a Year‌
• On the other hand, APY factors in the compounding frequency, explains the Consumer Financial Protection Bureau. Its formula is: ‌APY = ((1 + Periodic Rate)^ Number of periods) -1‌ or ‌APY = ((1+r/n )^n) -1‌, where r is the annual interest rate and n is the number of compounding periods.

Whether investing or taking out a loan, you should first consider the annualized interest rates. That way, you can compare the rate of return for an investment or the cost of borrowing across multiple products to get a better idea of whether you are getting a good deal.

Because APR only factors in the number of periods each year, you simply multiply the periodic rate by the number of periods. What you obtain as the total represents an annual basis. It is sometimes referred to as a simple interest rate.

For example, if someone offers to loan you money at ‌two percent‌ monthly interest rate and monthly payments, based on the formula, the APR is:

‌APR = 2 percent * 12‌, which equals ‌24 percent.‌ So, in this case, you could say you obtained a personal loan at ‌24‌ ‌percent‌ APR.

If you were to borrow ‌$10,000‌ at ‌24 percent‌ APR, you would owe ‌$2,400‌ as interest, or ‌$200‌ per month.

Suppose you made an investment with similar rates as above. In that case, if you were calculating APY:

‌APY = ((1+(2/100))^12) - 1‌ which is like ‌1.0212 - 1‌ and equal to ‌0.2682,‌ or ‌26.82 percent‌.

Therefore, your investments would have an APY of ‌26.82 percent‌.

So, if you were to invest ‌$10,000‌ at an APY of ‌26.82 percent‌, you would make ‌$2,682‌ as interest in a year, or ‌$223.50‌ per month. That would be enough to offset the monthly debts stated above.

Now, suppose you made another investment at similar rates, except this time around, the number of times interest gets compounded is twice a month. In that case, your annual percentage yield would be:

‌APY = ((1+ (0.02/2))^24) - 1‌, which is like ‌1.0124 - 1‌ and equal to ‌0.2697,‌ or ‌26.97 percent‌.

As you can see from this latest example, the more times compounding happens, the higher the overall APY, which means you would make higher returns.

Therefore, if you were to invest ‌$10,000‌, you would make ‌$2,697.34‌ per year, or an average of ‌$224.78‌ per month as interest.

When it is used, the APR works on your money negatively by reducing the amount you have each year since the interest is paid to another person or entity. However, it is stated in a way that makes your overall debt appear less over the long term.

Typically, the higher the annualized interest rate and the greater the number of compounding periods, the larger an amount becomes. If it is a debt, it can eventually spiral out of control, which is common among people who carry credit card balances that have high interest rates. According to Debt.org, a typical American individual has ‌3.8‌ credit cards and ‌$5,525‌ worth of credit card debt.

That said, the easiest way to determine your interest rates is to annualize them. By doing so, you get an idea of what you pay over the course of a year. Learning how to calculate annual equivalent rates can be helpful for keeping your personal finances in check.

APY is the yearly interest rate set for your investments, such as savings in a bank account. It is usually expressed as a percentage and is based on a one-year period. People sometimes refer to it as the effective annual interest rate, or EAR.

It is worth noting that the annualized interest rate, expressed as APY, usually considers the compound interest that has occurred over the course of that year. For example, if you invest in a bond that accrues interest twice a year, your annualized interest rate would be based on two compounding periods (12 months/6 months). Generally, the more compounding periods there are in a year, the more interest your investments earn, even when compared to another investment with a similar annualized interest rate.

On the other hand, the Corporate Finance Institute notes that APR usually represents the stated interest rates for any debts you take on, such as a mortgage or credit card balance. It’s mostly used by lenders (who are legally obligated to disclose it up front) because it does not consider the compounding of interest within a given year. Instead, it factors in the number of periods each year.