Name: Calculation of Compounded Amount
Uploaded: 2019-07-19
Duration: 9 min 18 s
Description: The two types of interest are - simple and compound. Let's calculate the total amount for a principal when the interest is compounded annually and half yearly.

Question

Ankita borrowed a certain amount of money from Parijat for two years at simple interest. Parijat lent the same amount of money to Sanchit at compound interest for two years. At the end of

2

years, Parijat received

₹ 110

as compound interest and

₹ 100

for simple interest. Find the amount given to each person and the rate of interests.

Accepted Answer

Let the sum borrowed by Ankita be $₹ P$ and rate of interest be $R %$ p.a

Simple interest $(S I) = ₹ 100$ , Time $(T) = 2$ years

$S I = \frac{P \times R \times T}{100}$

$100 = \frac{P \times R \times 2}{100}$

$P = \frac{5000}{R}$ ................(i)

Now, Parijat lent the same amount of money to Sanchit at compound interest for two years

$C I = P [{(1 + \frac{R}{100})}^{2} - 1]$

$110 = \frac{5000}{R} [{(\frac{100 + R}{100})}^{2} - 1]$

$11 R = 500 (\frac{10000 + R^{2} + 200 R - 10000}{10000})$

$11 R = 500 (\frac{R^{2} + 200 R}{10000})$

$11 R = R (\frac{R + 200}{20})$

$220 = R + 200$

$∴ R = 20 %$

From equation (i)

$P = \frac{5000}{20} = ₹ 250$

Therefore, the amount given to each person is $₹ 250$ and the rate of interest is $20 %$ .

Important Questions on Simple Interest and Compound Interest

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