# Amount when interest is compounded annually is given by the formula ______

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**Hint:**To solve this question, we should know the definition of compound interest, and some formulas to calculate the terms associated with the compound interest. Compound interest is the addition of the interest to the principal sum of a loan, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.

**Complete step by step answer:**

For this question, we will need the formula to calculate the amount gain in compound interest. The formula is \[A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}\]. Here, A is the amount gain, P is the principal amount, r is the interest, n is the number of times interest is compounded in a time period, t is the time period.

If we take an example for understanding it, then the principal \[=2p\] and rate \[=R\%\] per annum and the time \[=n\] years.

For the given problem, we have principal \[=2p\], rate of interest as \[R\%\] so \[r=\dfrac{R}{100}\], time period is n years, as we are compounded annually the value of n is 1.

Substituting these values in the above formula, we get,

\[\begin{align}

& A=2p{{\left( 1+\dfrac{\dfrac{R}{100}}{1} \right)}^{n}} \\

& A=2p{{\left( 1+\dfrac{R}{100} \right)}^{n}} \\

\end{align}\]

So, here is the value of the amount.

**Note:**We should also know the basic difference between the simple interest and compound interest. Simple interest is calculated on the principal, or original, amount of a loan.

Compound interest is calculated on the principal amount and also on accumulated interest of previous periods, and can thus be regarded as interest on interest.

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