Question

find the amount and the compound interest on 15000 for 2 years at 12% p.a compounded annually.​

Answer 1

GiveN:-

• Principal = Rs.15000
• Rate = 12%
• Time = 2 years

To FinD:-

The amount and compound interest.

SolutioN:-

We know that,

$\normalsize{\purple{\underline{\boxed{\bf{Amount=P\left(1+\dfrac{R}{100}\right)^n}}}}}$

where,

• P = principal = Rs.15,000
• R = rate = 12%
• n = time = 2 years

Putting the values,

$\\ :\normalsize\implies{\sf{Amount=15000\left(1+\dfrac{12\%}{100}\right)^2}}$

$\\ :\normalsize\implies{\sf{Amount=15000\left(1+\dfrac{\cancel{12}}{\cancel{100}}\right)^2}}$

$\\ :\normalsize\implies{\sf{Amount=15000\left(1+\dfrac{3}{25}\right)^2}}$

$\\ :\normalsize\implies{\sf{Amount=15000\left(\dfrac{25+3}{25}\right)^2}}$

$\\ :\normalsize\implies{\sf{Amount=15000\left(\dfrac{28}{25}\right)^2}}$

$\\ :\normalsize\implies{\sf{Amount=15000\left(\dfrac{28}{25}\times\dfrac{28}{25}\right)}}$

$\\ :\normalsize\implies{\sf{Amount=15000\times\dfrac{28}{25}\times\dfrac{28}{25}}}$

$\\ :\normalsize\implies{\sf{Amount=\cancel{15000}\times\dfrac{28}{\cancel{25}}\times\dfrac{28}{25}}}$

$\\ :\normalsize\implies{\sf{Amount=600\times28\times\dfrac{28}{25}}}$

$\\ :\normalsize\implies{\sf{Amount=\cancel{600}\times28\times\dfrac{28}{\cancel{25}}}}$

$\\ :\normalsize\implies{\sf{Amount=24\times28\times28}}$

$\\ \normalsize\quad\quad\therefore\boxed{\mathfrak{\pink{Amount=Rs.18,816.}}}$

Now the Compound Interest :

We know that,

$\normalsize{\purple{\underline{\boxed{\bf{Compound\:Interest=Amount-Principal}}}}}$

where,

• Amount = Rs.18,816
• Principal = Rs.15,000

Putting the values,

$\\ :\normalsize\implies{\sf{Compound\:Interest=Rs.(18816-15000)}}$

$\\ \normalsize\quad\therefore\boxed{\mathfrak{\pink{Compound\:Interest=Rs.3,816.}}}$

Amount = Rs.18,816.

Compound Interest = Rs.3,816.

Answer 2

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