The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

Effective Rates and The Truth in Lending Act

Under most circumstances, financial institutions must disclose the effective rate for deposit

accounts. The nominal rate may or may not be given, but the effective rate usually must

be. The point of requiring this is to enable consumers to readily compare different rates

without being confused by the effects of different compounding frequencies.

The Truth in Lending Act (also known as Regulation Z) is the main federal law in the

United States that requires financial institutions to make these disclosures. The regulations

that require this, however, are complex, and the terms effective rate or equivalent annual

rate will not generally be used. The most common term for the effective rates when deal-

ing with deposit accounts is APY, or annual(ized) percent yield. Depending on the type of

financial institution and type of deposit, investment, or loan, various different terms may

be used, including:

Annual percentage yield (APY)

Effective rate

Effective yield

Effective annual rate

Annualized yield

and so on.

Matters are made worse by the fact that in some cases the rate labeled as the APY may

not actually match what we would have calculated as the effective rate, if the financial prod-

uct requires payments of certain types of fees, or if the interest rate can vary in the future.

The full details fall far outside the scope of this book. However, it is important to recognize

that by whatever name it is given, this rate is intended as a means of “apples to apples” com-

parison. In many cases it will simply be the effective rate that we have been using. But even

when it is not, the purpose of this disclosure is to allow the consumer to compare the overall

interest rates being offered from different financial institutions and/or products.

It should also be noted that similar rules apply to the rates for loans as well as deposits.

With loans, the term “APR” (annual percentage rate) is often used. However, since most

loans require payments to be made during their terms, compounding is not quite so straight-

forward as with deposits. The APR for a loan is not the same as the APY for a deposit.

However, the “apples to apples” purpose is pretty much the same.

Normally, though, when we are talking about deposit accounts, the term APY will be

used, and unless the type of account has some unusual fees required or “bonuses” offered,

the APY will correspond to the effective rate as we have been discussing it. This example

is typical of how nominal and effective rates may be presented side by side:

Account Type Interest Rate APY

Interest Checking

Premium Checking

Premium Select Savings

CD 3 months–1 year

CD 1 year–3 years

CD 3 years–10 years

0.88%

1.25%

1.85%

2.45%

3.10%

3.65%

0.88%

1.26%

1.88%

2.48%

3.15%

3.72%

Again, the purpose of this disclosure is to make comparisons easier. If another bank is

offering a nominal rate of 3.66% for a 5-year CD, we can’t really tell from this whether or

not that rate beats the one offered in the table above, since we don’t know the compounding

frequencies, and even if we did we cannot directly compare nominal rates with different

frequencies. However, if we know that the APY for a 5-year CD at that other bank is 3.69%,

we can directly compare that to the APY shown above and see that the competing bank’s

interest rates are in fact a bit lower.

3.3 Effective Interest Rates 119