Question

b. 6,400 for 2 years at 6 % per annum compounded annually​

Answer 1

Given:

• Principle = Rs.6400
• Rate = 6% p.a.c.a
• Time = 2 years.

To Find:

• Amount = ?

Formula used:

$\\\bigstar{\underline{\boxed{\bf{ \red{A= P\bigg[1 + \dfrac{ {R}}{100} \bigg]^{T}}}}}}$

Solution:

★finding compound interest:

$\\{ \dashrightarrow \: {\sf{A= P\bigg(1 + \dfrac{ {R}}{100} \bigg)^{T}}}}$

${\dashrightarrow{\sf{A= 6400\bigg(1 + \dfrac{6}{100} \bigg)^{2}}}}$

${\dashrightarrow{\sf{A= 6400\bigg(\dfrac{(1 \times 100) + (6 \times 1)}{100} \bigg)^{2}}}}$

${\dashrightarrow{\sf{A= 6400\bigg(\dfrac{100 + 6}{100} \bigg)^{2}}}}$

${\dashrightarrow{\sf{A= 6400\bigg( \: \dfrac{106}{100} \: \bigg)^{2}}}}$

${\dashrightarrow{\sf{A= 6400\bigg( \dfrac{106}{100} \times \dfrac{106}{100} \bigg)}}}$

${\dashrightarrow{\sf{A= 6400\bigg(\dfrac{106 \times 106}{100 \times 100} \bigg)}}}$

${\dashrightarrow{\sf{A= 6400\bigg(\dfrac{11236}{10000} \bigg)}}}$

${\dashrightarrow{\sf{A= 6400 \times \dfrac{11236}{10000}}}}$

${\dashrightarrow{\sf{A= 6400 \times \cancel{\dfrac{11236}{10000}}}}}$

${\dashrightarrow{\sf{A= 6400 \times 1.1236}}}$

${\dashrightarrow{\sf{\purple{A= Rs. \:7,191.04 }}}}$

Hence, the amount is Rs.7,191.04.

★compound interest

$\\{\dashrightarrow{\sf{{C.I=A- P}}}}$

${\dashrightarrow{\sf{{C.I=7,191.04 - 6400}}}}$

${\dashrightarrow{\sf{\purple{C.I=Rs.791.04}}}}$

Hence, the compound interest is Rs.791.04