Question

Find the CI, if Rs 5000 was invested for 2 years at 10% p.a. compounded half-yearly?

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Answer 1

Given:

• A sum of Rs 5000 was invested for 2 years at 10% p.a. compounded half - yearly.

To Find:

• The compound Interest.

Solution:

★ Firstly, we have to find the amount:

According, to the question by using the formula, we get:

`\longmapsto \: { \bold{ \boxed{\pink{ \rm{A \: = P \left( 1 + ( (r)/(2) )/(100) \right)^(2n) }}}}}`

Here,

• Amount (A) = A
• Principal (P) = Rs 5000
• Rate of Interest (r) = 10% p.a
• Time Period (n) = 2 years

So by putting their values, we get:

`{ \large{\longrightarrow{ \rm{A = 5000 \left( 1 + ( (10)/(2) )/(100) \right)^(2 * 2) }}}}`

`{ \large{ \longrightarrow{ \rm{A = 5000 \left( 1 + (10)/(2) * (1)/(100) \right)^(4) }}}}`

`{\large{ \longrightarrow{ \rm{A = 5000 \left( 1 + (10 * 1)/(2 * 100) \right)^(4) }}}}`

`{ \large{ \longrightarrow{ \rm{A = 5000 \left(1 + (10)/(200) \right)^(4) }}}}`

`{ \large \longrightarrow {\rm{A =5000 \left( (200 * 1 + 10)/(200) \right)^(4) }}}`

`{ \large \longrightarrow{ \rm{A = 5000 \left( (200 + 10)/(200) \right)^(4) }}}`

`{ \large{ \longrightarrow{ \rm{A = 5000 \left( (210)/(200) \right)^(4) }}}}`

`{ \large{ \longrightarrow{ \rm{A = 5000 \left( (210)/(200) * (210)/(200) * (210)/(200) * (210)/(200) \right)}}}}`

`{ \large{ \longrightarrow{ \rm{A = 5000 \left( (210 * 210 * 210 * 210)/(200 * 200 * 200 * 200) \right)}}}}`

`{ \large{ \longrightarrow{ \rm{A = 5000 \left( (1944810000)/(1600000000) \right)}}}}`

`{ \large{ \longrightarrow{ \rm{A = 5000 * (1944810000)/(1600000000) }}}}`

`{ \large{ \longrightarrow{ \rm{A = 5000 * (194481)/(160000) }}}}`

`{ \large{ \longrightarrow{ \rm{A = 5 * (194481)/(160) }}}}`

`{ \large{ \longrightarrow{ \rm{A = (972405)/(160) }}}}`

`{ \large{ \longrightarrow{ \rm{A = 6077.53 \: (approx.)}}}}`

Hence, the amount is Rs 6078.

★ Now, we have to find the compound Interest:

According, to the question by using the formula, we get:

`{ \large{ \dashrightarrow{ \boxed{\green{ \rm{Compound \: Interest = A \: - \: P}}}}}}`

Here,

• Amount (A) = Rs 6078
• Principal (P) = Rs 5000

So, by putting their values we get:-

`{ \large{ \dashrightarrow{ \rm{Compound \: Interest = Rs \: 6078 \: - \: Rs \: 5000}}}}`

`{ \large{ \dashrightarrow{ \rm{Compound \: Interest = Rs \: 1078}}}}`

Hence, Compound Interest is Rs 1078.