Question

find the difference between the compound interest and simple interest on a sum of 10000 at the rate of 10% p.a for 2 years (compounded annually)​

Answer 1

let the rate of interest be 10% per annum

compound interest of ₹10000 in 2 yrs

like this

Answer 2

$\huge{\underline{\underline{\bf{Answer}}}}$

Given :-

• Principal = 10,000
• Rate% = 10%p.a
• Time Period = 2 year

To finD :-

• Difference between Compound interest and simple interest

Explanation :-

$\Large{\underline{\sf{\red{Finding\: Compound\: Interest :-}}}}$

[In question, Amount is not given so before finding Compound Interest, we have to find Amount]

$\large{\sf {\pink{[Formula\: Used= \: A= P(1 + { \frac{r}{100} })^{n} ]}}}$

Where,

• A = Amount
• P = principal
• r = rate%
• n = Time period

${\Large{\sf{\green{Substituting\: the\: values\: in \: Formula =}}}}$

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

${\sf{ A = 10000(1 + { \frac{10}{100} })^{2}}}$

${\sf { A = 10000{ (\frac{110}{100} })^{2}}}$

${\sf{ A = 10000 \times \frac{110}{100} \times \frac{110}{100} }}$

${\sf{A = 110 \times 110}}$

${\sf{A = 12100}}$

So, the amount = 12100

Compound Interest = A - P

Compound Interest = 12100 - 10000

= 2100

$\Large{\underline{\sf{\red{Finding\: Simple\: Interest :-}}}}$

${\sf {\pink{[Formula\: Used = S.I = \frac{P \times R \times T}{100}] }}}$

Where,

• S.I = Simple interest
• P = Principal
• R = Rate%
• T = Time Period

${\Large{\sf{\green{Substituting\: the\: values\: in \: Formula =}}}}$

${\sf{S.I = \frac{P \times R \times T}{100}}}$

${\sf { S.I = \frac{10000 \times 10\times 2}{100}}}$

${\sf{ S.I = 100 \times 10 \times 2}}$

${\sf{S.I = 2000}}$

${\huge{\sf{\blue{Finding\: Difference\: between\: C.I\: and\:S.I}}}}$

Difference between C.I and S.I = C.I - S.I

=> 2100 - 2000

=> 100rs

So,

Difference between C.I and S.I = rs 100