Effective annual rate calculator

Type the rate the way it was offered to you and see what it's worth as an effective annual rate, the only figure that compares.

Type of rate

NominalEffective annualPer period

Rate

Compounded

Paid

In arrearsIn advance

At the end of the period

Annual inflation (optional)

It's worth

12.68%E.A.

Your rate: 12% NMV

Effective monthly (EM): 1.00%
Effective quarterly (ET): 3.03%
Nominal, monthly in arrears (NMV)your rate: 12.00%
Nominal, quarterly in arrears (NTV): 12.12%
Nominal, monthly in advance (NMA): 11.88%
Interest on 1,000,000 in a year: 126,825 pesos

An educational tool: it converts rates, it doesn't project the results of any investment. Taxes and fees aren't included.

The abbreviations you'll see

Colombian banks publish the same rate under different codes. Here's what each one means.

E.A.

Effective annual

What your money really adds up to in a year, with interest earned on interest.

Effective monthly

What it adds up to in a month. Compounded twelve times, it gives the EAR.

Effective quarterly

What it adds up to in three months.

NMV

Nominal, monthly in arrears

An annual rate split across 12 months, paid at the end of each one.

NTV

Nominal, quarterly in arrears

Split across 4 quarters. NSV and NAV are the same per six months and per year.

NMA

Nominal, monthly in advance

Paid at the start of each month, so for the same EAR the figure is lower.

How it's worked out

1
Split the nominal rate across the periods
12% nominal monthly is 1% a month (12 / 12). Quarterly would be 3% a quarter (12 / 4).
2
If it's paid in advance, turn it into arrears
Paying 1% at the start of the month is worth the same as paying 0.01 ÷ (1 − 0.01) = 1.0101% at the end.
3
Compound the periods of the year
EAR = (1 + the period's rate) to the number of periods, minus 1. With 1% a month: 1.01¹² − 1 = 12.68%.

The formula, for rates paid in arrears

EAR=(1+jn)n−1

If the rate is paid in advance: EAR = (1 − j ÷ n)⁻ⁿ − 1

Where

EAR: the effective annual rate
j: the nominal annual rate, as a decimal (12% = 0.12)
n: the periods in a year: 12 if monthly, 4 if quarterly, 2 if every six months

With 12% nominal monthly

12.68%=(1+0.1212)12−1

Frequently asked questions

What's the difference between a nominal and an effective annual rate?

A nominal rate is an annual reference rate split across the periods of the year. The effective annual rate (EAR) includes the interest each period's interest earns, so it shows what your money adds up to in a year. That's why two products only compare well in EAR.

How do I turn an EAR into a monthly rate?

Add 1 to the EAR, take the twelfth root and subtract 1. For example, 10% EAR is 1.10 to the power of 1/12, minus 1: 0.797% a month. Multiplying 0.797% by 12 gives 9.57% nominal monthly, the nominal rate that produces that EAR.

Why is a rate paid in advance worth more?

Because you get the interest at the start of the period and can use it from that day. With the same figure, 12% monthly in advance is 12.82% EAR, and 12% monthly in arrears is 12.68% EAR.

What's the real rate?

What's left after inflation: (1 + EAR) ÷ (1 + inflation) − 1. With 9% EAR and 5% inflation, the real rate is 3.81%. Subtracting them directly (4%) slightly overstates it.