Question

Simple interest on a sum of money for 2 years at 4% is 450/-. Find the compound interest on the same sum and at the same rate for 2 years.

Answer 1

Step-by-step explanation:

The formula for SI = Pnr/100

Given SI = Rs. 450, n = 2 and r = 4%, we have

450 = 2*4*P/100

Or P = 450*100/(2*4) = 5625.

CI for the same interest rate for 1 year, compounded every half yearly can be given by the formula

A = P(1+r/100)^n.

Here, P = 5625, r = 4/2 = 2% and n = 2, since there are two half-yearly compounding of the amounts.

Thus A = 5625*(1+2/100)^2 = 5625*1.02)^2 = 5625*1.0404 = 5852.25

Therefore, the compound interest is A - P = 5852.25-5625 = 227.25.

Thus, the CI for Rs. 5625 at 4% compounded half-yearly is Rs. 227.25.

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is Rs 459

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$\huge\sf\blue{Given}$

✭ Simple interest (S.I.) on a sum of money = 450 Rs

✭ Time period , t = 2 years

✭ Rate of interest , R = 4 %

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$\huge\sf\gray{To \:Find}$

◈ Compound interest (C.I.) on the same sum of money at the same rate and for the same time of 2 years

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$\huge\sf\purple{Steps}$

Simple Interest of a data is found by,

$\underline{\boxed{\sf{S.I.=\frac{P\times R\times t}{100}}}}$

Compound Interest of a data can be found by,

$\underline{\boxed{\sf{C.I.=P\left(1+\dfrac{R}{100}\right)^{t} - P}}}$

Calculating Principle Money

$\twoheadrightarrow\sf{S.I.=\dfrac{P\times R\times t}{100}}\\\\\twoheadrightarrow\sf{450=\dfrac{P\times 4 \times 2}{100}}\\\\\twoheadrightarrow\sf{P=\dfrac{45000}{4\times2}}\\\\\twoheadrightarrow\red{\sf{P=5625\:Rs}}$

Now calculating C.I. on P = 5625 Rs , R = 4 % , t = 2 yrs

$\dashrightarrow\sf{C.I.=P\bigg\lgroup 1+\dfrac{R}{100}\bigg\rgroup^t-P}\\\\\dashrightarrow\sf{C.I=5625\bigg\lgroup 1 + \dfrac{4}{100}\bigg\rgroup^2-5625}\\\\\dashrightarrow\sf{C.I.=5625\bigg\lgroup 1+\dfrac{16}{10000}+\dfrac{8}{100}\bigg\rgroup-5625}\\\\\dashrightarrow\sf{C.I=5625\bigg\lgroup1+\dfrac{16}{10000}+\dfrac{8}{100}-1\bigg\rgroup}\\\\\dashrightarrow\sf{C.I.=5625\bigg\lgroup\dfrac{16+800}{10000}\bigg\rgroup}\\\\\dashrightarrow\sf{C.I=\dfrac{5625\times 816}{10000}}\\\\\dashrightarrow\sf{C.I=\dfrac{4590000}{10000}}\\\\\dashrightarrow\orange{\sf{C.I=459\:Rs}}$

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