Question

find the compound interest on rs. 2000 for one year at the rate of 20% per annum if the interest compounded quarterly.​

Answer 1

S O L U T I O N :

Given :

• Principal, (P) = Rs.2000
• Rate, (R) = 20% p.a
• Time, (n) = 1 year

Explanation :

As we know that formula of the compounded quarterly:

• A = P(1 + R/4/100)^4n

According to the question :

➝ A = P(1 + R/4/100)^4n

➝ A = 2000(1 + 20/4 × 100)^4 × 1

➝ A = 2000(1 + 20/400)⁴

➝ A = 2000(1 + 1/20)⁴

➝ A = 2000(20 + 1/20)⁴

➝ A = 2000(21/20)⁴

➝ A = 2000 × 21/20 × 21/20 × 21/20 × 21/20

➝ A = 5 × 21 × 21 × 21 × 21/400

➝ A = 972405/400

➝ A = Rs.2431.01

Now, as we know that compound Interest :

➝ C.I. = Amount - Principal

➝ C.I. = Rs.2431.01 - Rs.2000

➝ C.I. = Rs.431.01

Thus,

The compound Interest will be Rs.431.01 .

Answer 2

$\huge \boxed {\frak{Answer:}}$

$\large \bold{Given:- }$

$\sf \longrightarrow{Principal,P =₹2,000 }$

$\sf \longrightarrow{Rate,R=20\% }$

$\sf \longrightarrow{Time,n =1year }$

$\large \bold{To \: find:- }$

$\leadsto \sf{Compound \: interest \: in \: quarterly}$

$\large \bold{Formula \: required:}$

$\sf{A = P\Bigg \{{1 + \frac{R}{4} } \times 100 \Bigg \} ^{4n} }$

$\large \bold{According \: to \: Question:- }$

$\sf{A = P\Bigg \{{1 + \frac{R}{4} } \times 100 \Bigg \} ^{4n} }$

$\sf{A = P\Bigg \{{1 + \frac{20}{4} } \times 100 \Bigg \} ^{4n} }$

$\sf{A = 2000\Bigg \{{{1 + \frac{20}{400} \Bigg \}}} ^{4 \times 1}}$

$\sf{A = 2000\Bigg \{{{1 + \frac{1}{20} \Bigg \}}} ^{4} }$

$\sf{A = 2000 \Bigg \{{ \frac{21}{20} \Bigg \}} ^{4}}$

$\sf{A = 2000 \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} }$

$\sf{A = \frac{1,94,481}{80} = ₹2,431.01 }$

C. I.=Amount-Principal

C. I.=₹2,431.01-₹2,000=₹431.01