Question

Find the amount and compound intrest on Rs625000 for 1 year at the rate of 8% p.a compounded half yearly

Answer 1

Solution :

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

• Principal, (P) = Rs.625000
• Rate, (R) = 8% p.a.
• Time, (n) = 1 year

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

Using formula of the compounded half-yearly;

$\boxed{\bf{Amount=Principal\bigg(1+\frac{R}{2\times 100} \bigg)^{2n}}}$

A/q

$\mapsto\sf{A=625000\bigg(1+\dfrac{\cancel{8} }{\cancel{2} \times 100} \bigg)^{(2\times 1)}}\\\\\\\mapsto\sf{A=625000\bigg(1+\cancel{\dfrac{4}{100}} \bigg)^{2}}\\\\\\\mapsto\sf{A=625000\bigg(1+\dfrac{1}{25} \bigg)^{2}}\\\\\\\mapsto\sf{A=625000\bigg(\dfrac{25+1}{25} \bigg)^{2}}\\\\\\\mapsto\sf{A=625000\bigg(\dfrac{26}{25} \bigg)^{2}}\\\\\\\mapsto\sf{A=\cancel{625000} \times \dfrac{26}{\cancel{25}}\times \dfrac{26}{\cancel{25}} }\\\\\\\mapsto\sf{A=Rs.(1000 \times 26\times 26)}$

$\mapsto\bf{A=Rs.676000}$

Now, as we know that compound Interest;

⇒ C.I. = Amount - Principal

⇒ C.I. = Rs.676000 - Rs.625000

⇒ C.I. = Rs.51000

Thus;

The amount & compound Interest will be Rs.676000 & Rs.51000 .

Answer 2

Answer:

Solution :

Given:

Principal, (P) = Rs.625000

Rate, (R) = 8% p.a.

Time, (n) = 1 year

Explanation:

Using formula of the compounded half-yearly;

{Amount=Principal(1+frac{R}{2\times 100}{2n}

Amount=Principal(1+

2×100

R

)

2n

A/q

\begin{gathered}\mapsto\sf{A=625000\bigg(1+\dfrac{\cancel{8} }{\cancel{2} \times 100} \bigg)^{(2\times 1)}}\\\\\\\mapsto\sf{A=625000\bigg(1+\cancel{\dfrac{4}{100}} \bigg)^{2}}\\\\\\\mapsto\sf{A=625000\bigg(1+\dfrac{1}{25} \bigg)^{2}}\\\\\\\mapsto\sf{A=625000\bigg(\dfrac{25+1}{25} \bigg)^{2}}\\\\\\\mapsto\sf{A=625000\bigg(\dfrac{26}{25} \bigg)^{2}}\\\\\\\mapsto\sf{A=\cancel{625000} \times \dfrac{26}{\cancel{25}}\times \dfrac{26}{\cancel{25}} }\\\\\\\mapsto\sf{A=Rs.(1000 \times 26\times 26)}\\\\\end{gathered}

↦A=625000(1+

2

×100

8

)

(2×1)

↦A=625000(1+

100

4

)

2

↦A=625000(1+

25

1

)

2

↦A=625000(

25

25+1

)

2

↦A=625000(

25

26

)

2

↦A=

625000

×

25

26

×

25

26

↦A=Rs.(1000×26×26)

\mapsto\bf{A=Rs.676000}↦A=Rs.676000

Now, as we know that compound Interest;

⇒ C.I. = Amount - Principal

⇒ C.I. = Rs.676000 - Rs.625000

⇒ C.I. = Rs.51000

Thus;

The amount & compound Interest will be Rs.676000 & Rs.51000 .