Effective annual vs. nominal rate: how to compare a CDT without mistakes

By Camilo Tirado · 5-minute read

One bank offers you a CDT at 11.5% N.M.V. and another at 12% E.A. Which pays more? If you answered “the 12% one”, you were wrong… narrowly: the first is equivalent to 12.13% E.A. The difference lies in how the rate is stated, and understanding it keeps you from comparing apples and oranges.

The effective annual rate: the one to compare with

The effective annual rate (E.A., efectiva anual) measures how much your money grows in a year if the interest is reinvested. If you invest COP 10,000,000 at 12% E.A., after one year you have COP 11,200,000, no matter whether the interest was calculated monthly, quarterly or at the end.

That is why it is the measure for comparisons: two investments with the same E.A. rate earn the same in a year.

The nominal rate: a number you have to “translate”

A nominal rate is an annual rate that is divided among the periods of the year. “12% N.M.V.” means “nominal, monthly, in arrears”: each month you are paid 12% ÷ 12 = 1% on the balance, at the end of the month. Since that interest in turn earns interest, the actual growth over a year is more than 12%:

E.A. = (1 + 0.12 ÷ 12)¹² − 1 = 12.68%

The Colombian abbreviations all follow the same pattern: N.M.V. (monthly, in arrears), N.T.V. (quarterly, in arrears), N.S.V. (semiannual, in arrears) and, when interest is charged at the start of the period, N.M.A. or N.T.A. (in advance).

How to convert one into the other

If m is the number of periods in a year (12 monthly, 4 quarterly, 2 semiannual):

from nominal to E.A.: E.A. = (1 + nominal ÷ m)^m − 1

from E.A. to nominal: nominal = m × ((1 + E.A.)^1/m − 1)

Rate offered	Equivalent to
12% E.A.	11.39% N.M.V. · 11.49% N.T.V.
11.5% N.M.V.	12.13% E.A.
12% N.T.V.	12.55% E.A.
11% N.T.A.	11.80% E.A.

What about rates in advance?

With a rate in advance, interest is charged or paid at the start of the period. It is common in some loans. For the same nominal number, a rate in advance is more expensive (if you are the borrower) than one in arrears, because you pay earlier. To convert it to a rate in arrears:

periodic rate in arrears = periodic rate in advance ÷ (1 − periodic rate in advance)

Three common mistakes

Comparing an E.A. rate with a nominal rate as if they were the same.
Dividing the E.A. rate by 12 to get the monthly rate: 12% ÷ 12 = 1% is not right; the equivalent monthly rate is 0.949%.
Forgetting taxes and inflation. A good E.A. rate can shrink to very little after withholding tax and inflation. We cover it in how much a CDT really pays.

Run the numbers with your own rates in the free rate converter.

Keep learning

Module 1 of the course: why fixed income is not “fixed”

How to read any rate in the Colombian market, what you buy when you buy a bond and why your statement moves, with interactive examples. Launch price with the coupon LANZAMIENTO20, already applied in the button, until November 8.

See the course