Calculating Effective Annual Interest Rate from Nominal Interest Ratte

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dzafar

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Hi,

I am taking an engineering economics course. The questions says:

Suppose I have an effective interest rate – 10% per month,
compounded monthly, say – and I want to transform it
to an equivalent effective annual rate. How do I do this?

How I approached this problem was using:

ia = (1+(r/m))m - 1​

where,
r: nominal interest rate per year
m: number of compounding sub-periods per year​

But doing so gives me r = 120%. But shouldn't it always be less than or equal to 99?

Any help appreciated!
 


I wish I could find an investment that pays 10% monthly. For every dollar invested, (1+0.10)^12 = $3.13843 or 313.843% interest annually.

Ratch
 

As a check, multiply 1.1 * 1.1 and repeat to accumulate twelve times. See what is the net total.

Or, test your formula with other interest rates, especially much greater than 10%. Example, 20%, 100%. See what is the net total.
 

The formula to convert the interest rate over "k" periods to the annual interest is:

i = (1+ik)^k - 1

where i is the annual interest
ik is the interest over "k" periods, that is i2 is semestral, i6 bimestral, i12 monthly.

In your case i = (1+ 0.1)^12 - 1 = 2.14 that is 214%

this number doesn't have to be limited to 100%
 

Use 1 as the base; after one month it becomes 1.1 (10% interest per month)

After 12 months this becomes (1.1)^(12); 3.138428377

The interest is 3.138428377-1=2.138428377 and the effective annual rate is 213.84%
 

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