Question

Let us calculate the compound interest and amount on Rs.1600 for 1 whole 1/2 years at the rate of 10% compound interest per annum compounded at the interval of 6 months.​

Answer 1

${ \underline{ \underline{ \green{ \bf{Given : }}}}}$

P(principal) = ₹1,600

r(rate) = 10%.

n(time) = 1½ years.

${ \underline{ \underline{ \green{ \bf{To \: find : }}}}}$

The compound interest which is compounded half - yearly.

${ \underline{ \underline{ \green{ \bf{Solution : }}}}}$

We know that,

${ \underline{ \boxed{ \blue{ \sf{amount = p (1 + { \frac{r}{100} }^{n} ) }}}}}$

Where,

P(principal) = ₹1,600

r(rate) = 5%.

n(time) = 3years.

Note :

as it is compounded half yearly therefore, rate is divided by 2 and time is 3 years.

✧ Procedure :

Substituting the given values as follows :

$\dashrightarrow \sf \: a = 1600(1 + { \frac{ \cancel5}{ \cancel{100}} )}^{3} \\ \dashrightarrow \sf \: a = 1600 \times (1 + \frac{1}{20} {)}^{3} \\ \dashrightarrow \sf \: a = 16 \cancel {00} \times \frac{21}{20} \times \frac{21}{2 \cancel 0} \times \frac{21}{\cancel{20}} \\ \dashrightarrow \sf \: a = 178.2$

We also know that :

➠ C. I. = Amount - Principal

➠ C. I. = 1768.2 - 1,600

➠ C. I. = 168.2 ans.