Question

9. Find the difference between compound
interest and simple interest on 12,000 and
H
in 1
years at 10% p.a. compounded yearly.
2
10. Find the difference between compound
interest and simple interest on * 12,000 and
C
in 1
years at 10% compounded half-yealry.
2
BY USING AMOUNT FORMUL
A​

Answer 1

Sᴏʟᴜᴛɪᴏɴ ❾ :-

As we know That, In first year Simple interest and compound interest are same.

So,

Difference between compound interest and simple interest on 12,000 in 1 years at 10% p.a. compounded yearly will be Zero.

No Need to Solve Here.

________________________

Sᴏʟᴜᴛɪᴏɴ ❿ :-

→ Principal = Rs.12000

→ Rate = 10% compounded half-yealry = 5% .

→ Time = 1 Year. = 1 * 2 = 2 Year.

So,

→ SI = (P * R * T)/100

→ SI = (12000 * 5 * 2)/100

→ SI = Rs.1200 .

And,

→ CI = P[{(1 + R/100)² - 1}]

→ CI = 12000 * [{( 1 + 5/100)² - 1}]

→ CI = 12000 * [(21/20)² - 1]

→ CI = 12000 * (441 - 400)/400

→ CI = (12000 * 41)/400

→ CI = Rs.1230 .

Hence,

→ Diff. b/w CI & SI = 1230 - 1200 = Rs.30 (Ans.)

_______________________

Extra :-

If You want to Solve with Direct Formula :-

☛ Diff. b/w CI & SI = P * (Rate)² / (100)². { only when Time is 2 Years.)

Putting values Now, we get :-

☞ Diff. b/w CI & SI = (12000 * 5²) / (100 * 100)

☞ Diff. b/w CI & SI = (12 * 25) / 10

☞ Diff. b/w CI & SI = (300/10)

☞ Diff. b/w CI & SI = Rs.30 (Ans.)

______________________

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \purple{Question:-}}}}}}$

▪ Find the difference between compound interest and simple interest on Rs. 12,000 in 1 year at 10 %

( i ) when compounded yearly

( ii ) when compounded half- yearly

${ \huge{ \bold{ \underline{ \underline{ { \purple{Solution:-}}}}}}}$

${ \bold{ \underline{ \blue{Given-}}}}$

▪ Principal ( P ) = Rs. 12,000

▪ Time ( T ) = 1 year

▪ Rate ( R ) = 10%

${ \bold{ \underline{ \blue{To \: find-}}}}$

▪ Difference between compound interest and simple interest??

${ \bold{ \red{(i) \: when \: compounded \: yearly}}}$

We know that ,

In the first year , the simple and compound interest on a certain sum is same.

thus, the difference between compound interest and simple interest when compounded yearly for 1 year is equal to zero...

${ \bold{ \red{(ii) \: when \: compounded \: half \: yearly}}}$

here,

▪ R = (10/2)% = 5%

▪ T = 2×1 year = 2 year

☆ Simple interest ( S.I.)

${ \boxed{ \bold{ \blue{ \: S.I. = \frac{P \times R \times T \: }{100} }}}}$

${ \bold{ \implies{S.I. = \frac{12000 \times 5 \times 2}{100} }}}$

${ \bold{ \implies{S .I. = 120 \times 10}}}$

${ \boxed{ \bold{ \implies{ \red{ \: S.I. = Rs . \: 1200 \: \: }}}}}$




☆ Compound Interest ( C.I.)


${ \boxed{ \bold{ \blue{C .I . = P(( {1 + \frac{R}{100} )}^{T} - 1)}}}}$


${ \bold{ \implies{C.I . = 12000( ({1 + \frac{5}{100} )}^{2} - 1)}}}$

${ \bold{ \implies{C .I. = 12000(( {1 + \frac{1}{20} )}^{2} - 1)}}}$

${ \bold{ \implies{C .I. = 12000( ({ \frac{21}{20} )}^{2} - 1)}}}$

${ \bold{ \implies{C .I . = 12000( \frac{441}{400} - 1)}}}$

${ \bold{ \implies{C .I. = 12000( \frac{441 - 400}{400}) }}}$

${ \bold{ \implies{C.I. = 12000 \times \frac{41}{400} }}}$

${ \bold{ \implies{C.I. = 30 \times 41}}}$

${ \boxed{ \bold{ \implies{ \red{ \: C.I . = Rs . \: 1230 \: \: }}}}}$

${ \star{ \bold{ \: \: difference \: between \: C.I. \: and \: S.I .}}}$

${ \bold{ \blue{ \: = \: C.I. - S.I . \: }}}$

${ \bold{ \blue{ = Rs . \: 1230 - \: Rs. \: 1200}}}$

${ \huge{ \boxed{ \bold{ \red{ \: \: Rs . \: 30 \: }}}}}$