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Understanding the Math of Returns

 

Each Country or institution has a different way to present the percentage of the returns to their investors, and it is good to understand it to avoid surprises.

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Frist, the meaning of the acronyms.

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• AER: It stands for Annual Equivalent Rate. This figure shows what the interest rate would be if interest was paid and compounded on an annual basis.

• P.A.: It stands for Per Annum. This figure shows the simple interest rate.

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In European Countries is very common you see P.A. or AER. Specially AER when your investments has daily, monthly and quarterly payments.

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In South American Countries is very common, if your investments has monthly payments, the interest rate is showed per month.

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What are the differences mathematically?

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Per Annum (Simple Interest)

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Amount Invested = $1.000,00

Interest Rate P.A. = 10%

Returns after 1 year = $100

Total Amount after 1 year = $1.100,00

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Per Month (Compound Interest)

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Amount Invested = $1.000,00

Interest Rate P.M. = 0,8333%

 

Returns after 1 month= $8,33 ($1000 x 8,333%)

Total Amount after 1 month = $1.008,33

 

Returns after 1 year = $8,33 ($1000 x 8,333%)

Total Amount after 1 year = $1.008,33

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Simple Interest Formula

Simple Interest = P × i × n

P=Principal
i=Interest rate
n=Term of the loan
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Compound Interest Formula

 

A = Final amount
P = Initial principal balance
r = Interest rate
n = Number of times

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