Compound Interest Compounded Yearly

When interest is compounded yearly, the interest earned at the end of each year is added to the principal before calculating the next year's interest. If a sum of $P$ is invested at $r\%$ per annum for $t$ years, compounded yearly, the amount at the end of $t$ years is

and the compound interest is $CI = A - P$.

Why the formula looks this way: at the end of Year 1 the amount is $P\left(1+\dfrac{r}{100}\right)$. This becomes the new principal for Year 2, so the amount at the end of Year 2 is $P\left(1+\dfrac{r}{100}\right)^{2}$. Repeating this build-up for $t$ years gives the formula above — this is exactly the interest-on-interest idea from the previous section, made precise.