Interest rate converter

Type a rate in any form and see its equivalent as an effective annual rate, a nominal rate in arrears, a nominal rate in advance and a periodic rate.

Rate (%)For example 12 or 11.5

That rate is…

Payment or compounding period

Effective annual—

Nominal, in arrears—

Nominal, in advance—

Period rate, in arrears—

Period rate, in advance—

Why there are so many ways to state the same rate

In Colombia, CDTs (certificates of deposit), loans and bonds are quoted in different ways: one bank advertises “12% E.A.”, another “11.39% N.M.V.” and a bond pays a “quarterly coupon”. They can be exactly the same return. The only fair way to compare them is to convert them all to an effective annual rate (E.A., efectiva anual), which measures how much your money grows in a year if you reinvest the interest.

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

The formulas

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

periodic rate = (1 + E.A.)^1/m − 1

nominal in arrears = m × periodic rate

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

E.A. = (1 + nominal ÷ m)^m − 1

An example with a CDT

A COP 10,000,000 CDT at 12% E.A. that pays interest every quarter has a quarterly rate of (1.12)^1/4 − 1 = 2.874%, that is, 11.49% N.T.V. Each quarter it pays you about COP 287,400 before taxes. If you are offered another CDT at 11.6% N.T.V., that one pays slightly more: it is equivalent to 12.12% E.A.

Watch out for the words “in advance”: with a rate in advance, interest is deducted at the start of the period, so for the same nominal number the effective rate is higher than with a rate in arrears.

In the course

The full converter and the module “Why fixed income is not ‘fixed’”

The course includes the full version of this converter, with exact days, and the lesson that explains how to read any rate in the Colombian market. Launch price with the coupon LANZAMIENTO20, already applied in the button, until November 8.

See the course