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### Equivalent interest rates

Equivalent interest rates are those that, when applied to the same capital, in the same period, produce equal values.
A principal (P) applied at a rate (i1) for a period (n) produces an amount (S) . If the same capital applied to a different rate (i2) to produce the same amount, we say that the rates are equivalents.
See, how to get the generic formula.
By the definition of equivalent rates, as above, we have:
S = S1.
r = i / 100 (Interest rate in decimal form)
S = P (1 + ra) (annual rate)
S1 = P (1 + rm) 12 (monthly rate)
As we know, by definition, S = S1
P (1 + ra) = P (1 + rm) 12,
1 + ra = (1 + rm) 12
ra = (1 + rm) 12 -1
Example:
Be the monthly interest rate of 2%, what is the equivalent annual rate?
ra = (1 + rm) 12 - 1
ra = (1 +0.02) 12 -1
ra = (1.02) 12 -1
ra = 1.2682 -1
ra = 0.2682 or 26.82%
Finally, the generic formula for calculating the equivalent rates:
r1 = {(1+r2) (n1/n2)} -1
r1 = requested interest rate;
r2 = known interest rate;
n1 = period corresponding to the desired rate;
n2 = period corresponding to the known rate.
How to calculateEquivalent interest rates.