Question

If the simple interest on a certain sum for 1.5 years at 8% p.a. is 360. Find the compound interest on the same sum for the same rate of interest but double the time​

Answer 1

$Let \: the \: Principal = Rs \:P$

$Rate \:of \: interest (R) = 8% ,\\Time (T) = 1.5 \:years ,\\Simple \: interest (I) = Rs\:360$

$\boxed { \pink { P = \frac{100\times I}{TR} }}$

$\implies P = \frac{ 100\times 360}{1.5 \times 8}\\= Rs \:3000$

$\underline { Finding \: Compound \: Interest: }}$

$Principal (P) = Rs \: 3000 , \\Time (T) = 3 \: years , \\Rate (R) = 8\% , conversation \:periods (n) = 3$

$Let \: Amount = Rs \:A$

$\boxed { \orange { A = P\left( 1 + \frac{R}{100}\right)^{n} }}$

$\implies A = 3000\left( 1 + \frac{8}{100}\right)^{3}\\= 3000 \left( \frac{108}{100}\right)^{3} \\= 3000 \times \frac{108}{100} \times \frac{108}{100} \times \frac{108}{100}$

$= Rs \: 3779.136$

$Now, \red{ Compound \: interest } = A - P \\= Rs\: 3779.136 - Rs \: 3000 \\= Rs \: 779.136$

Therefore.,

$\red {Compound \: interest } \green {=Rs \: 779.136}$

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Answer 2

Answer:

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