Question

Find the compound interest on Rs. 1000 at the rate of 20% p.a. for 18 month when interest is compounded half yearly.​

Answer 1

Answer:

compound interest = Rs. 331.

Answer 2

${ \large{ \underline{ \pmb{ \sf{Given...}}}}}$

★ Amount of Rupees 1000 is compounded half yearly at the rate 20% for 18 months.

${ \large{ \underline{ \pmb{ \sf{To \: Find ...}}}}}$

★ The Compound interest on the sum of money

${ \large{ \underline{ \pmb{ \sf{Solution...}}}}}$

★ The Compound interest on the following sum of money is Rs.331

${ \large{ \underline{ \pmb{ \sf{Full \: Solution...}}}}}$

~ As we have the principal amount , time, rate of interest and also know that it is compounded half - yearly. Let's use the formula to find the amount when compounded half- yearly and leter subtract the principal from it to find the compound Interest

↦ Formula :

$\: \: \: \: \: \: \dag \: \bigg[ \bf \:A = P \bigg(1 + \frac{r}{200} \bigg){}^{2n} \bigg ]$

➼ Where,

• A denotes Amount
• P denotes Principal
• R denotes Rate
• N denotes Time[ No. of years]

~ Now let's substitute the values of the following in the formula mentioned above and find the amount.

${ : \implies} \sf \: Amount = principal \bigg [1 + \frac{r}{200} \bigg ] {}^{2n} \\ \\ \\ { : \implies} \sf \: Amount = 1000 \bigg [ 1 + \frac{20}{200} \bigg ] {}^{2 \times \frac{1}{2} } \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: Amount = 1000 \bigg[ \frac{22 \cancel0}{20 \cancel0} \bigg ] {}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: Amount = 1000 \times \frac{22}{20} \times \frac{22}{20} \times \frac{22}{20} \\ \\ \\ { : \implies} \sf \: Amount = 11 \times 11 \times 11 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} { \boxed{ \pmb{ \frak{ Amount =1331 }}} \bigstar} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the amount is Rs. 1331

~ Now let's subtract the principal from the amount to find the compound interest

➼ C.I = Amount - Principal

➼ C.I = 1331 - 1000

➼ C.I = Rs.331

• Henceforth the compound Interest is Rs.331

${ \large{ \underline{ \pmb{ \sf{Additional \: Information ...}}}}}$

• Formula to find Amount interest when compounded annually

${ : \implies}\: \bigg[ \bf \:A = P \bigg(1 + \frac{r}{100} \bigg){}^{n} \bigg ]$

• Formula to find amount when compounded quarterly

${ : \implies}\: \bigg[ \bf \:A = P \bigg(1 + \frac{r}{200} \bigg){}^{2n} \bigg ]$