Question

the difference between compound interest and simple interest earned on a certain amount at 20% p.a at the end of 3 years is Rs 640. Find the Principal?​

Answer 1

Given:-

•Difference between Compound Interest and Simple Interest is 640 rupees.

•Rate of interest is 20% per annum.

•Time is given here 3 years.

To Find:-

•Principal on difference between Compound Interest and Simple Interest.

Solution:-

we have,

• Rate = 20%
• Time = 3 years

Let consider Principal amount be P.

Firstly we will find out Simple Interest

Using Formula:

$\: \: \sf \: simple \: interest = \frac{principal \times rate \times time}{100}$

Now substitute the values,

$\: \: \sf \: simple \: interest = \frac{ p \times 20 \times 3 }{100} \\ \\ \: \: \sf \: simple \: interest = \frac{60p}{100} = 0.6p$

Hence, Simple Interest is 0.6P.

Now we will find Compound Interest

Using Formula:

$\: \: \sf \: compound \: interest = amount - principal \\ \\ \: \: \sf \: compound \: interest = (p {(1 + \frac{r}{100}) }^{2} ) - p$

Now substitute the values,

$\: \: \sf \: compound \: interest = (p {(1 + \frac{20}{100} )}^{3} ) - p \\ \\ \: \: \sf \: compound \: interest = (p \times \frac{20}{100} \times \frac{20}{100} \times \frac{20}{100} ) - p \\ \\ \: \: \sf \: compound \: interest = (p \times 1.2 \times 1.2 \times 1.2) - p \\ \\ \: \: \sf \: compound \: interest = (1.728p) - p \\ \\ \: \: \sf \: compound \: interest = 0.728p$

Hence, Compound Interest is 0.728P.

Now we are given here difference between Compound Interest and Simple Interest is 640 rupees.

$\: \: \sf \: 0.728 - 0.6p = 640 \\ \\ \: \: \sf \: 0.128p = 640 \\ \\ \: \: \sf \: p = \frac{640}{0.128} \\ \\ \: \: \sf \: p = \frac{640 \times 1000}{128} \\ \\ \: \: \sf \: p = 5 \times 1000 \\ \\ \: \: \sf \: p = 5000 \: rupees$

$\therefore$Henceforth, Principal is 5000 rupees.

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Answer 2

Answer:

Step-by-step explanation:

We Know that

• Compound interest > Simple interest
• So,
• Difference = compound interest - simple interest
• OR
• D = C.I - S.I
• D = [p(1+i/m)^mn - p] - pin
• D = p [(1+i)^n - 1 - in]
• 640 = p[(1+0.2)^3 - 1 - (0.2)(3)
• By Solve on calculator :
• p = 5000