Question

The simple interest on a certain sum of money at 8% p.a. for 2 years is Rs 2160. If the interest is compounded annually.Find the compound interest.​

Answer 1

Answer:

• Compound interest is Rs 2246.4 .

Step-by-step explanation:

Given :-

• Rate of interest is 8%.
• Time period is 2 years.
• Simple interest is Rs 2160.

To find :-

• Compound interest.

Solution :-

• First we will find principal for finding compound interest. So, Using simple interest we will find principal.

$\boxed{\bold{Simple \: interest = \dfrac{P \times r \: times t}{100} }}$

Where,

• P is principal.
• r is rate of interest.
• t is time period.

Put values in formula :

$\sf \longrightarrow 2160 = \dfrac{P \times 8 \times 2}{100}$

$\sf \longrightarrow 2160 \times 100 = P \times 16$

$\sf \longrightarrow 216000 = P \times 16$

$\sf \longrightarrow \dfrac{216000}{16} = P$

$\sf \longrightarrow \bold{P = 13500}$

Principal is Rs 13500.

Now,

Interest is compounded annually.

So,

We know,

Compound interest = Amount - Principal

Or,

$\boxed{\bold{Compound \: interest = \bigg\{ P \bigg( 1 + \dfrac{r}{100} \bigg)^{n} \bigg\} - P}}$

Where,

• P is principal.
• r is rate of interest.
• n is time period.

Put all values :

$\sf \longrightarrow Compound \: interest = \bigg\{ 13500 \times \bigg( 1 + \dfrac{8}{100} \bigg)^{2} \bigg\} - 13500$

$\sf \longrightarrow Compound \: interest = \bigg\{ 13500 \times \bigg( \dfrac{100 + 8}{100} \bigg)^{2} \bigg\} - 13500$

$\sf \longrightarrow Compound \: interest = \bigg\{ 13500 \times \bigg( \dfrac{108}{100} \bigg)^{2} \bigg\} - 13500$

$\sf \longrightarrow Compound \: interest = \bigg\{ 13500 \times \dfrac{11664}{10000} \bigg\} - 13500$

$\sf \longrightarrow Compound \: interest = \bigg\{13500 \times 1.1664 \bigg\} - 13500$

$\sf \longrightarrow Compound \: interest = 15746.4 - 13500$

$\sf \longrightarrow \bold{ Compound \: interest = 2246.4 }$

Therefore,

Compound interest is Rs 2246.4 .

Answer 2

Question :-

The simple interest on a certain sum of money at 8% p.a. for 2 years is Rs 2160. If the interest is compounded annually .Find the compound interest.​

Given :-

→ Rate of Interest = 8 % p.a.

→ Time period = 2 years

→ Simple Interest = Rs. 2160

To Find :-

→ The compound interest.​

Solution :-

→ As we know that ,

${ \boxed{\sf Simple\;Interest\;=\; \frac{P \times r \times t }{100} }}$

$\sf Where , \\\\P = Principal \\\\r = rate\;of\;interest\\\\t = time\; period$

$\sf \longrightarrow Rs. 2160 = \dfrac{P \times 8 \times 2}{100} \\\\\\\longrightarrow 2160 \times 100 = P \times 16\\\\\\\longrightarrow P = \dfrac{216000}{16} \\\\\\\longrightarrow P = 13500$

∴ Principal = Rs. 13500

→ As , the interest is compounded annually

→ We know that

${ \boxed{\sf Compound\;interest\;=\;Amount - Principal }}$

 or

${ \boxed{\sf Compound\;Interest\;= \{ P(1+\dfrac{r}{100})^{n} \} }}$

$\sf Where , \\\\P\; = \; principal.\\\\r\;=\;rate\;of\;interest.\\\\n\;=\;time\;period.$

→ Let's solve by substituting the values !!

$\sf \longrightarrow CI = \{ 13500 \times \bigg( 1 + \dfrac{8}{100} \bigg)^{2} \} -13500\\\\\\\longrightarrow CI = \{ 13500 \times \bigg( \dfrac{100+8}{100} \bigg) ^{2} \}-13500\\\\\\\longrightarrow CI = \bigg\{ 13500 \times \bigg(\dfrac{108}{100} \bigg)^{2}} \bigg\} -13500 \\\\\\\longrightarrow CI = \bigg\{ 13500 \times \dfrac{11664}{10000} \bigg\} -13500\\\\\\\\\longrightarrow CI = \bigg\{ 13500 \times 1.1664 \bigg \} - 13500 \\\\\\\longrightarrow CI = 15746.4 - 13500$

$\sf { \underline{Compound\;Interest\;=\; 2246.4}}$

All Done ! :D