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Normally, you have an interest rate, r, over some specified period (typically a month, quarter or year) and an amount Y that is invested (or loaned) for n periods. Then the total value, V, of the investment is:

V = Y*(1 + r/100)^n

It is possible to chop up the total time interval into smaller intervals and adjust the interest rate correspondingly so that the total percentage change over a year remains the same. The above equation then takes the form

V = Y*e^ax

The statement in the question simply means that, instead of calculating the interest using the first formula, it is calculated using the second. The interest is then paid out every three months and so every three months the capital returns to the value Y.

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Q: What does it mean by interest is compounded continuously and paid quarterly?
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