Question

Find the amount and the compound interest on ₹16,000 for 3 years at 5% per annum compounded annually.

Don't copied Answer.​

Answer 1

$\large\bold{\underline{\underline{Answer:-}}}$

$\underline{\bf{Given\::}}$

Principal, (P) = Rs.16000

Rate, (R) = 5% p.a

Time, (n) = 3 years

$\underline{\bf{Explanation\::}}$

As we know that formula of the compounded annually;

$\boxed{\bf{Amount = Principal\bigg(1+\frac{R}{100} \bigg)^{n}}}$

A/q

$\mapsto\tt{A = P\bigg(1+\dfrac{R}{100} \bigg)^{n}}$

$\mapsto\tt{A =16000 \bigg(1+\dfrac{5}{100} \bigg)^{3}}$

$\mapsto\tt{A =16000 \bigg(1+\cancel{\dfrac{5}{100} }\bigg)^{3}}$

$\mapsto\tt{A =16000 \bigg(1+\dfrac{1}{20} \bigg)^{3}}$

$\mapsto\tt{A =16000 \bigg(\dfrac{20+1}{20} \bigg)^{3}}$

$\mapsto\tt{A =16000 \bigg(\dfrac{21}{20} \bigg)^{3}}$

$\mapsto\tt{A =16000\times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20} }$

$\mapsto\tt{A =\cancel{16000} \times \dfrac{21}{\cancel{20}} \times \dfrac{21}{\cancel{20}} \times \dfrac{21}{\cancel{20}} }$

$\mapsto\tt{A = Rs.(2 \times 21 \times 21 \times 21)}$

$\mapsto\bf{A = Rs.18522}$

Now, as we know that compound Interest;

→ C.I. = Amount - Principal

→ C.I. = Rs.18522 - Rs.16000

→ C.I. = Rs.2522

Therefore,

The amount & compound Interest will be Rs.18522 & Rs.2522 .

Answer 2

Principal = (P) = ₹16, 000

Time = (t) = 3 years

Rate = (r) = 5%

Amount = Principal × (1 + (r/2 × 100)) n × 2

= ₹ 16,000 × (1+ (5/200)) 3 × 2

= ₹16,000 × (205/200)6

= ₹ 16,000 × 41/40 × 41/40 × 41/40 × 41/40 × 41/40 × 41/40

= ₹ 18,555

C.I. = Amount – Principal

= ₹ 18,555 - ₹ 16,000

₹ 2555