Question

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$\textsf {Prove that the difference between the compound interest and}$
$\sf {simple \: interest \: for \: 2 \: years \: is \: P({ \dfrac{ {R}^{2} }{10000}}}).$


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Answer 1

Hey Mate!! Got ur answer,hope it helps.

Answer 2

Answer:

PR²/10000

Step-by-step explanation:

Simple Interest:

We know that SI = PTR/100.

Interest for 2 years = (PR * 2/100)

                               = PR/50.

Compound Interest:

We know that CI = P(1 + R/100)ⁿ - P

Interest for 2 years = P(1 + R/100)² - P

= P[(1 + R/100)² - 1]

= P[(1 + 2R/100 + R²/10000) - 1]

= P(2R/100 + R²/10000)

= (2PR/100) + (PR²/10000)

= (PR/50) + (PR²/10000)

∴ Difference between Compound Interest and Simple Interest:

= (PR/50) + (PR²/10000) - (PR/50)

= (PR²/10000).

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