Annual Percentage Yield

It identifies the real rate of return obtained from related financial products

You may see APY figures on a range of savings and investment products in the financial world. It identifies the real rate of return you will obtain from related financial products as the APY equation includes the compounding interest valuation.

The annual percentage yield (APY) may also be displayed as the effective annual interest rate (EAR).

Compound interest works by adding interest payments to the initial balance or principal payment to be included in the following interest calculation, equating to a more significant interest payment than the last.

The more frequent compounding occurs, for instance, daily, monthly, or quarterly, the greater the exponential effect compounding has on interest. Daily compounding would multiply interest faster than monthly compounding.

A larger balance would accumulate significantly more compound interest over time than a smaller balance.

On the other hand, simple interest calculates the annual rate of return using the whole deposit sum when no premium interest is added to the account balance.

The formula below represents the percentage of growth acquired from compound interest, assuming money has been deposited for an entire year:

APY = ((1 + R/N)^N) - 1

R = period rate

N = number of compounding periods

How can Annual Percentage Yield be used?

Investments are made attractive through their rate of return. A high APY would demonstrate a high investment growth rate. The compound frequency would attribute to the APY percentage.

When investments in a portfolio present different compounding periods and APYs, it can be confusing and difficult to calculate the exact return on investments.

The main identifiers that provide a good overview of compound interest investments are high APY and more frequent compounding periods.

An investment can grow faster if regular deposits are added to the overall balance, as a larger balance would generate greater compound interest payments.

Investments that benefit from compound interest:

APY example (single year)

You are unsure between two investment options, a one-year zero-coupon bond generating a 12% return upon maturity or a high-yield money market account providing a monthly rate of 1% with monthly compounding.

The perception of most individuals would likely assume the yields are equal as 12 (months) multiplied by the 1% monthly rate equates to 12%.

However, the monthly compounding effect reveals the money market account accumulates a better return on investment, 12.68%, as shown below:

APY = ((1 + 0.01)^12) - 1)

APY = 12.68%

APY example (multiple years)

A deposit of $200 into a savings account that accumulates a 0.5% interest monthly and is compounded monthly provides an annual account total of $212.34. In contrast, simple interest would have sustained a total of $212.

APY = ((1+0.005)^12)) - 1

APY = 6.17%

Total account balance = $200(1.061677812)

Total account balance = $212.34

An annual interest rate of 6% compounded monthly provides a real rate of 6.17%, which can significantly impact the return on savings over a more extended period.

If the interest rate remained constant after one year and the individual kept $200 in the savings account for five years, the total account balance would be $269.77.

Simple interest would show a total of $260. The difference between compound and simple interest is more apparent after five years.

X = D (1 + r/n)^(n*y)

= $100(1 + .005)^(12*5)

= $100(1.348850153)

X = $269.77

Where:

X = Final amount

D = Initial Deposit

r = period rate 

n = number of compounding periods per year

y = number of years

If regular deposits were made during the five years, the equation would become more complex but would provide greater returns.

A larger initial deposit would better utilize the exponential rate of return.

APY vs. APR

The annual percentage rate (APR) is the percentage a borrower pays to a lender as interest in addition to the loan's principal. The percentage can include servicing fees but does not account for compound interest, representing simple interest.

Likewise, APY is not inclusive of servicing fees as the calculation provides compounding results.

Financial institutions advertise their savings and investment products using APY instead of APR, as APY presents the larger actual return on investments provided the compounding characteristics.

The frequency of compounding periods should be considered before comparing APY as products with equivalent compounding frequencies, but different APYs will help identify the better investment opportunity.

When compounding interest is more frequent, a larger difference is visible between APY and APR.

Again as servicing fees are not included in the APY, it would be best to find out if there are any additional servicing fees.

Contrarily, lenders flaunt APR as it masks the real interest rate on loans, making it more appealing to borrowers. The conditions of compounding interest on loans must be thoroughly understood before borrowing, especially with mortgages.

Borrowers always look for the lowest possible rate and the most reasonable amortization costs when acquiring a loan. This can be relevant to credit card transactions, mortgage loans, or personal loans.

An interest rate promoted as APR instead of APY shows the initial lower rate, disguising multiplier charges that may arise with compounding periods that are later disclosed to the client.

Banks quote an APR on loans, which does not account for the compounding interest and its frequency period, whether semi-annually, quarterly or monthly.

Compounding interest can significantly weigh on annual payments made towards a mortgage loan which are typically 6-figure sums and can mature over 30 years.

Analysis

A large loan would increase the interest payments exponentially, providing additional funds to the bank. On the other hand, larger and more frequent principal and interest payments towards a loan would notably reduce its compounding effect.

Both APR and APY are subject to change, influenced primarily by the federal funds rate, voted by the Federal Open Market Committee(FOMC).

Interest rates are used as a monetary policy to moderate inflation, with the target rate for inflation set at 2%. High inflation causes the purchasing power of money to weaken rapidly as a result of excessive growth.

An increase in the Fed rate would hike interest rates; consequently, APR and APY benefit lenders more than borrowers as they would experience greater returns. This restricts the amount of money being borrowed and spent, cooling inflation as economic growth contracts.

Whereas a decrease would lower interest rates and benefit borrowers more than lenders as it would be less costly to pay off loans, stimulating economic growth.

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Researched and authored by Rohan HiraniLinkedIn

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