Question

8. Ms Patel invests Rs 80,000 at a compound interest rate of 10% p.a. for 2 years while Ms Kapoor
invests Rs 1,00,000 at a compound interest rate of 8% for 3 years. Who will earn more and by how
much?
​

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Case ❶ :-

→ Principal = P = Rs.80000

→ Rate = 10%

→ Time = 2 years.

→ CI = P[{1 + R/100}^T - 1]

→ CI = 80000[{1 + 10/100}² - 1]

→ CI = 80000 * [(11/10)² - 1]

→ CI = 80000 * (121 - 100/100)

→ CI = 80000 * 21/100

→ CI = Rs.16,800

Case ❷ :-

→ Principal = P = Rs.100000

→ Rate = 8%

→ Time = 3 years.

→ CI = P[{1 + R/100}^T - 1]

→ CI = 100000[{1 + 8/100}³ - 1]

→ CI = 100000 * [(27/25)³ - 1]

→ CI = 100000 * (27³ - 25³)/25³

→ CI = 100000 * (4058/15625)

→ CI = Rs.25971.2

Hence,

→ Ms. Kapoor Earn More = 25971.2 - 16800 = Rs.9171.2 (Ans.)

Answer 2

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

Compound Interest ( C.I.)

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

${ \orange{ \bold{ \underline{given-}}}}$

${ \bold{ \underline{investment \: of \: Ms \: Patel :}}}$

▪ Principal (P) = Rs. 80,000

▪ Rate (R) = 10% per annum

▪time (T) = 2 years

C.I. on Ms. Patel's investment--

${ \bold{C.I.(P) = 80000{ {((1 + \frac{10}{100} )}^{2} - 1)}}}$

${ \bold{ \implies{C.I.(P ) = 80000 { {(( \frac{11}{10} )}^{2} - 1)}}}}$

${ \bold{ \implies{C .I .(P ) = 80000( \frac{121}{100} - 1)}}}$

${ \bold{ \implies{C.I .(P) = 80000( \frac{121 - 100}{100} )}}}$

${ \bold{ \implies{C.I .(P) = 80000 \times \frac{21}{100} }}}$

${ \pink {\bold{ \implies{ C.I.(P ) = 16800}}}}$

therefore,

Compound Interest on Ms. Patel' s investment

= Rs. 16,800

${ \bold{ \underline{ investment \: of \: ms \: kapoor}}}$

▪ Principal (P) = Rs. 1,00,000

▪ Rate ( R ) = 8% p.a

▪ time ( T) = 3 years

C.I. on Ms. kapoor's investment --

${ \bold{C.I .(K ) = 100000( {(1 + \frac{8}{100} )}^{3} - 1)}}$

${ \bold{ \implies{C .I .(K) = 100000 ( {(1 + \frac{2}{25}) }^{3} - 1)}}}$

${ \bold{ \implies{C.I.(K ) = 100000( ({ \frac{27}{25} }^{3} ) - 1)}}}$

${ \bold{ \implies{C .I .(K) = 100000( \frac{19683}{15625} - 1)}}}$

${ \bold{ \implies{C .I.(K) = 100000 \times \frac{(19683 - 15625)}{15625} )}}}$

${ \bold{ \implies{C .I.(K ) = 100000 \times \frac{4058}{16525} }}}$

${ \pink {\bold{ \implies{C .I .(K) = 25971.2}}}}$

Compound Interest on Ms. kapoor's investment = Rs. 25971.2

since,

Compound Interest on Ms. kapoor's investment is more than that of Ms. Patel's

= Rs. 25971.2 - Rs. 16800 = Rs. 9171.2

thus,

Ms. kapoor Will earn more... by Rs. 9,171.2