Question

When principal $P$ is compounded semi-annually at $r\%$ per annum for $t$ years, then Amount = ______

Answer 1

Find the Amount.

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. Compound interest is calculated as:

$\mathrm{Compound}\mathrm{Interest}=\mathrm{Amount}-\mathrm{Principal}$

Amount, $A$ is calculated as $A=P{\left(1+\frac{r}{n}\right)}^{nt}$

Where,

$A=$ amount

$P=$ principal

$r=$ rate of interest

$n=$ number of times interest is compounded per year

$t=$ time (in years)

If the compound interest is calculated semi annually at $r\%$ per annum for $t$ years then the Amount, $A$ is

$A=P{\left(1+\frac{r}{200}\right)}^{2t}$

Therefore, when principal $P$ is compounded semi-annually at $r\%$ per annum for $t$ years, then amount, $A$ is

$A=P{\left(1+\frac{r}{200}\right)}^{2t}$