Compound interest is calculated on the current balance, including earlier interest. With a positive fixed rate and no deposits or withdrawals, the interest earned increases from period to period. $A=P{{(1+\frac{R}{100})}^{n}}$ The total amount is $A$, and the compound interest earned is $A-P$. Use the interest method stated in the question. If the method or compounding frequency is not specified, state an assumption or obtain clarification; missing words alone do not establish simple interest. Let’s see what will the interest be on $\$1500$ for $4$ years at given that $5\%$ per annum if it is compounded yearly, monthly, half-yearly and quarterly. Compounded No of periods Interest rate for each period Amount at the end of 4 years Interest earned $1$ yearly Period (yearly) $n=4$ $5\%$ $R=5$ ${A = 1500\left(1 + \frac{5}{100}\right)^4}$ ${A = 1823.26}$ ${A - P}$ = $\$323.26$ $2$ monthly $4$ years $\times 12$months $=48$months $n=48$ $1$ year $\to 5\%$ $1$ month $\to \frac{5}{12}\%$ $R=\frac{5}{12}$ ${A = 1500\left(1 + \frac{5/12}{100}\right)^{48}}$ $A$ = $\$1831.34$ ${A - P}$ = $\$331.34$ $3$ half yearly 6 months bi-annually $4$years $\times 2$ =$8$ halves of a year $n=8$ $1$ year $\to 5\%$ $\frac{1}{2}$ year $\to \frac{5}{2}\%$ $R=\frac{5}{2}$ ${A = 1500\left(1 + \frac{5/2}{100}\right)^{8}}$ $A$ = $\$1827.60$ ${A - P}$ = $\$327.60$ $4$ quarterly $1$ year $\to 4$quarters $4$years $=4\times 4$ quarters $=16$ $n=16$ $1$ year $\to 5\%$ $\frac{1}{4}$ year $\to \frac{5}{4}\%$ $R=\frac{5}{4}$ ${A = 1500\left(1 + \frac{5/4}{100}\right)^{16}}$ $A$ = $\$1829.83$ ${A - P}$ = $\$329.83$ Correction to the retained scan: interest earned is $A-P$, not $P-A$. Do not infer simple interest solely because the word compounded is absent. The examples use a nominal annual rate split across the stated compounding periods.

Compound Interest

Secondary 3

Compound interest is calculated on the current balance, including earlier interest. With a positive fixed rate and no deposits or withdrawals, the interest earned increases from period to period.

$A=P{{(1+\frac{R}{100})}^{n}}$

The total amount is $A$, and the compound interest earned is $A-P$.

Use the interest method stated in the question. If the method or compounding frequency is not specified, state an assumption or obtain clarification; missing words alone do not establish simple interest.

Let’s see what will the interest be on $\$1500$ for $4$ years at given that $5\%$ per annum if it is compounded yearly, monthly, half-yearly and quarterly.

	Compounded	No of periods	Interest rate for each period	Amount at the end of 4 years	Interest earned
$1$	yearly	Period (yearly) $n=4$	$5\%$ $R=5$	${A = 1500\left(1 + \frac{5}{100}\right)^4}$ ${A = 1823.26}$	${A - P}$ = $\$323.26$
$2$	monthly	$4$ years $\times 12$months $=48$months $n=48$	$1$ year $\to 5\%$ $1$ month $\to \frac{5}{12}\%$ $R=\frac{5}{12}$	${A = 1500\left(1 + \frac{5/12}{100}\right)^{48}}$ $A$ = $\$1831.34$	${A - P}$ = $\$331.34$
$3$	half yearly 6 months bi-annually	$4$years $\times 2$ =$8$ halves of a year $n=8$	$1$ year $\to 5\%$ $\frac{1}{2}$ year $\to \frac{5}{2}\%$ $R=\frac{5}{2}$	${A = 1500\left(1 + \frac{5/2}{100}\right)^{8}}$ $A$ = $\$1827.60$	${A - P}$ = $\$327.60$
$4$	quarterly $1$ year $\to 4$quarters	$4$years $=4\times 4$ quarters $=16$ $n=16$	$1$ year $\to 5\%$ $\frac{1}{4}$ year $\to \frac{5}{4}\%$ $R=\frac{5}{4}$	${A = 1500\left(1 + \frac{5/4}{100}\right)^{16}}$ $A$ = $\$1829.83$	${A - P}$ = $\$329.83$

Correction to the retained scan: interest earned is $A-P$, not $P-A$. Do not infer simple interest solely because the word compounded is absent. The examples use a nominal annual rate split across the stated compounding periods.

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	Compounded	No of periods	Interest rate for each period	Amount at the end of 4 years	Interest earned
\(1\)	yearly	Period (yearly) \(n=4\)	\(5\%\) \(R=5\)	\({A = 1500\left(1 + \frac{5}{100}\right)^4}\) \({A = 1823.26}\)	\({A - P}\) = \(\$323.26\)
\(2\)	monthly	\(4\) years \(\times 12\)months \(=48\)months \(n=48\)	\(1\) year \(\to 5\%\) \(1\) month \(\to \frac{5}{12}\%\) \(R=\frac{5}{12}\)	\({A = 1500\left(1 + \frac{5/12}{100}\right)^{48}}\) \(A\) = \(\$1831.34\)	\({A - P}\) = \(\$331.34\)
\(3\)	half yearly 6 months bi-annually	\(4\)years \(\times 2\) =\(8\) halves of a year \(n=8\)	\(1\) year \(\to 5\%\) \(\frac{1}{2}\) year \(\to \frac{5}{2}\%\) \(R=\frac{5}{2}\)	\({A = 1500\left(1 + \frac{5/2}{100}\right)^{8}}\) \(A\) = \(\$1827.60\)	\({A - P}\) = \(\$327.60\)
\(4\)	quarterly \(1\) year \(\to 4\)quarters	\(4\)years \(=4\times 4\) quarters \(=16\) \(n=16\)	\(1\) year \(\to 5\%\) \(\frac{1}{4}\) year \(\to \frac{5}{4}\%\) \(R=\frac{5}{4}\)	\({A = 1500\left(1 + \frac{5/4}{100}\right)^{16}}\) \(A\) = \(\$1829.83\)	\({A - P}\) = \(\$329.83\)