Question

Find the compound interest if Rs. 4000 are invested for 3 years at the rate of 12 1/2 p.c.p.a.
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Answer 1

Given:

• Rs. 4000 are invested for 3 years at the rate of 12 1/2 p.c.p.a.

To Find:

• Compound interest

Solution:

Here, P = Rs. 4000; R = 12½%; N = 3 years

Therefore,

$\implies \sf{A = P\bigg(1 + \dfrac{R}{100} \bigg)^N }$

$\implies \sf{P \bigg( 1 + \dfrac{12.5}{100} \bigg)^3 }$

$\implies \sf{4000 \; \bigg( 1 + \dfrac{125}{10000} \bigg)^3}$

$\implies \sf{4000 \; \bigg( \dfrac{\cancel{1125}}{\cancel{1000}}\bigg)^3}$

$\implies \sf{4000 \; \bigg( \dfrac{9}{8} \bigg)^3}$

$\implies \boxed{\sf{\orange{Rs. \; 5695.31 }}}$

     

We know that,

$\dag \; \underline{\boxed{\sf{\purple{Compound \; interest = amount - principal}}}}$

   

∴ Compound Interest after three years,

$\implies \sf{I = Amount - Principal}$

$\implies \sf{5695.31 - 4000}$

$\implies \boxed{\sf{\orange{Rs. \; 1695.31}}}$

   

Final Answer:

━ The compound interest is Rs. 1695.31.

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* ⁺◦﹆◞˚ ꒰ More to know ꒱

⟢ Sometimes the interest is calculated at an interval of six months. For the duration of N years, if the rate is R and if the interest is to be calculated six-monthly then the rate is to be taken as R/2 and the duration is considered as 2N stages of six months.

⟢ Many banks charge the compound interest monthly. At that time they take the interest rate as R/12 monthly and the duration is taken 12 × N stages of months and interest is calculated.

⟢ Nowadays banks calculate compound interest daily.

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Answer 2

Compound Interest

Compound interest is the interest on interest. It is the addition of interest to the principal sum of a loan or deposit.

The amount can be calculated by using the following formula:

$\boxed{\bf{C.I. = P\Bigg[\bigg(1 + \frac{R}{100}\bigg)^{T}\Bigg]}}$

The compund interest can be calculated by using the following formula:

$\boxed{\bf{C.I. = A - P}}$

Where, CI is the Compund Interest, P is is the Principal Amount, R is the Rate of Interest and T is the Time Period.

We have to determine the Compund Interest, when Rs. 4000 are invested for 3 years at the rate of 12 1/2 p.c.p.a.

According to the given information, we have been given that,

• Principal amount, P = Rs. 4000
• Time period, T = 3 years
• Rate of interest, R = 12 1/2 = 12.5%
• Compound interest, CI = ?

By using the amount formula and substituting the given values, we obtain:

$\implies A = 4000\Bigg[\bigg(1 + \cancel{\dfrac{12.5}{100}}\bigg)^{3}\Bigg] \\ \\ \implies A = 4000\Bigg[\bigg(1 + \dfrac{1}{8}\bigg)^{3}\Bigg] \\ \\ \implies A = 4000\Bigg[\bigg(\dfrac{8 + 1}{8}\bigg)^{3}\Bigg] \\ \\ \implies A = 4000\Bigg[\bigg(\dfrac{9}{8}\bigg)^{3}\Bigg] \\ \\ \implies A = 4000\Bigg[\dfrac{729}{512}\Bigg] \\ \\ \implies A = \cancel{4000} \times \dfrac{729}{ \cancel{512}} \\ \\ \implies A = 7.8125 \times 729 \\ \\ \implies A = 5695.31$

Now by using the compound interest formula and substituting the known values, we get:

$\implies C.I. = 5695.31 - 4000 \\ \\ \implies \boxed{\bf{C.I. = 1695.31}}$

Hence, the compound interest is Rs. 1695.31.