Question

if
simple interest on a sum of money at 4% per annum for 6 years is 2400, find
the compound interest
on the same sum for the same period at the same rate.answer is £2653.19​

Answer 1

AnswEr :

$\bold{Given} \begin{cases} \sf{Simple \: Interest=Rs. 2400} \\ \sf{Rate=4\% \: p.a.} \\ \sf{Time=6 \: Yr.}\\ \sf{Principal=?}\end{cases}$

⇒ Simple Interest = PRT /100

⇒ 2400 = P × 4 × 6 /100

⇒ 2400 × 100 = P × 24

⇒ 240000 = 24P

⇒ P = 240000 /24

⇒ P = Rs. 10000

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$\bold{Now \: We \: Have} \begin{cases} \sf{Principal=Rs. 10000} \\ \sf{Rate=4\% \: p.a.} \\ \sf{Time=6 \: Yr.}\\ \sf{Compound \: Interest=?}\end{cases}$

$\leadsto\sf{CI = \bigg[P \bigg(1 + \dfrac{r}{100} \bigg)^{t} - 1 \bigg]}$

$\leadsto\sf{CI = \bigg[10000\bigg(1 + \cancel\dfrac{4}{100} \bigg)^{6} - 1 \bigg]}$

$\leadsto\sf{CI = \bigg[10000 \bigg(1 + \dfrac{1}{25} \bigg)^{6} - 1 \bigg]}$

$\leadsto\sf{CI = \bigg[10000 \bigg(\dfrac{26}{25} \bigg)^{6} - 1 \bigg]}$

$\leadsto\sf{CI = \bigg[10000 \bigg(\dfrac{308,915,776}{244,140,625} - 1 \bigg) \bigg]}$

$\leadsto\sf{CI = \bigg[10000 \times \dfrac{64,775,151}{244,140,625} \bigg]}$

$\leadsto\sf{CI = \bigg[10000 \times 0.265319 \bigg]}$

$\leadsto \large \boxed{\sf{CI =Rs. \: 2653.19}}$

⠀

∴ Compound Interest is Rs. 2653.19

Answer 2

Question :-

if simple interest on a sum of money at 4% per annum for 6 years is 2400, find

the compound interest on the same sum for the same period at the same rate.

Answer :-

→ Compound interest is Rs 2653.1902

To find :-

→ Compound interest .

Formula used :-

$\star \boxed{\sf \: \: { \pink{ Simple \: interest} \: = \frac{PRT}{100} } }\\ \\ \red{\sf{ \small \star \: Compound \: interest \:} = \green{ Amount \: - principal} }\\ \\ \star \boxed{\sf{ \pink{amount }\: = p { \red{ \bigg(1 + \frac{r}{100} \bigg) }^{t} }}}$

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Step - by - step explanation :-

Given that ,

• Rate ( R) = 4% p.a.

• Time ( T) = 6 years .

• Simple interest ( SI) = Rs.2400

• Principal ( P ) = ?

• Amount = ?

• Compound interest ( CI) = ?

Solution :-

Using the given formula for SI.

$\rightarrow \sf{ \green{2400 = \frac{P \times 4 \times 6}{100} }} \\ \\ \rightarrow \sf{ P \: \: = \frac{240000}{24} } \\ \\ \red{ \rightarrow \boxed{\sf{P \: (principal) = 10000}}}$

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$\rightarrow \red{\sf{Amount \: = 10000} \: \pink{ { \bigg(1 + \frac{4}{100} \bigg)}^{6} }} \\ \\ \rightarrow \sf{ Amount = 10000 { \green{ \bigg( { \frac{26}{25} \bigg) }^{6} } }}\\ \\ \rightarrow \sf{ \red{Amount \: } = \pink{10000 \times {(1.04)}^{6} }} \\ \\ \rightarrow \sf{ Amount \: = \red{10000 \times 1.26531902} }\\ \\ \rightarrow \boxed{ \sf{ \green{Amount \: = 12653.1902}}}$

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We know that ,

Compound interest = Amount- Principal

→ CI = 12653.1902 - 10,000

→ CI = Rs. 2653.1902

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