Question

Find the amount and CI on ₹6000 for 3 years at 10% per annum​

Answer 1

Answer:

Step-by-step explanation:

Given

Rate of interest = 10% per annum

Principal for the first year = Rs 6000

Interest for the first year = Rs (6000 × 10 × 1) / 100

= Rs 600

Amount at the end of first year = Rs 6000 + Rs 600

= Rs 6600

Principal for the second year = Rs 6600

Interest for the second year = Rs (6600 × 10 × 1) / 100

= Rs 660

Amount for the second year = Rs 6600 + Rs 660

= Rs 7260

Therefore, compound interest for 2 years = final amount – (original) Principal

= Rs 7260 – Rs 6000

We get,

= Rs 1260

Answer 2

Answer:

The amount and CI on the given principal are ₹ 7986 and ₹ 1986 respectively.

Step-by-step-explanation:

We have given that,

• Principal ( P ) = ₹ 6000
• Rate of interest ( R ) = 10 %
• Time period ( N ) = 3 years

We have to find the amount and compound interest ( CI ).

Now, we know that,

$\displaystyle{\boxed{\pink{\sf\:Amount\:=\:Principal\:\left(\:1\:+\:\dfrac{Rate\:of\:interest}{100}\:\right)^{Time\:period}\:}}}$

$\displaystyle{\implies\sf\:Amount\:=\:P\:\left(\:1\:+\:\dfrac{R}{100}\:\right)^N}$

$\displaystyle{\implies\sf\:Amount\:=\:6000\:\left(\:1\:+\:\dfrac{\cancel{10}}{\cancel{100}}\:\right)^3}$

$\displaystyle{\implies\sf\:Amount\:=\:6000\:\left(\:1\:+\:\dfrac{1}{10}\:\right)^3}$

$\displaystyle{\implies\sf\:Amount\:=\:6000\:\left(\:\dfrac{10\:+\:1}{10}\:\right)^3}$

$\displaystyle{\implies\sf\:Amount\:=\:6000\:\left(\:\dfrac{11}{10}\:\right)^3}$

$\displaystyle{\implies\sf\:Amount\:=\:6000\:\times\:\dfrac{11}{10}\:\times\:\dfrac{11}{10}\:\times\:\dfrac{11}{10}}$

$\displaystyle{\implies\sf\:Amount\:=\:\dfrac{\cancel{6000}\:\times\:11\:\times\:11\:\times\:11}{\cancel{1000}}}$

$\displaystyle{\implies\sf\:Amount\:=\:6\:\times\:11\:\times\:121}$

$\displaystyle{\implies\sf\:Amount\:=\:66\:\times\:121}$

$\displaystyle{\implies\sf\:Amount\:=\:(\:60\:+\:6\:)\:(\:120\:+\:1\:)}$

$\displaystyle{\implies\sf\:Amount\:=\:60\:(\:120\:+\:1\:)\:+\:6\:(\:120\:+\:1\:)}$

$\displaystyle{\implies\sf\:Amount\:=\:7200\:+\:60\:+\:720\:+\:6}$

$\displaystyle{\implies\sf\:Amount\:=\:7200\:+\:720\:+\:66}$

$\displaystyle{\implies\sf\:Amount\:=\:7920\:+\:66}$

$\displaystyle{\therefore\:\underline{\boxed{\green{\sf\:Amount\:=\:Rs.\:7986\:}}}}$

Now, we know that,

$\displaystyle{\boxed{\blue{\sf\:Compound\:interest\:=\:Amount\:-\:Principal\:}}}$

$\displaystyle{\implies\sf\:Compound\:interest\:=\:7986\:-\:6000}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:Compound\:interest\:=\:Rs.\:1986\:}}}}$

∴ The amount and CI on the given principal are ₹ 7986 and ₹ 1986 respectively.