Question

compute the compound interest on rupees thousand for 2 years at 10% per annum when compounded half yearly​

Answer 1

Answer:

ANSWER

Here, Principal P = Rs. 1000

R =10% per annum and n=2 years

∴ Amount after 2 years = P (1+

200

R

)

2n

= Rs. 1000×(1+

200

10

)

2×2

=Rs.1000×(1+

20

1

)

4

=Rs.1000×(

20

21

)

4

= Rs.1000×

20

21

×

20

21

×

20

21

×

20

21

=Rs.1215.50

Hence, compound interest = Amount - Principal

=Rs.1215.50−Rs.1000=Rs.215.50

Answer 2

Step-by-step explanation:

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

• Principal = Rs. 1000

• Rate = 10% per annum

• Time = 2 years

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• The Compound Interest compounded half - yearly.

$\bf\underline{\underline{\green{Solution:-}}}$

Principal = Rs. 1000

Rate = 10% per annum

For half - yearly Rate = 5%

Time = 2 years = 4 half-years

To find the Compound Interest, first we need to find the Amount

$\boxed {\rm \leadsto Amount = P\bigg( 1 + \dfrac{r}{100}\bigg)^{n}}$

Here:-

• P = Principal = Rs. 1000

• r = Rate = 5%

• n = Time = 4 half - years

$\rm = 1000\times \bigg( 1 + \dfrac{5}{100}\bigg)^{4}$

$\rm = 1000\times \bigg( \dfrac{100+5}{100}\bigg)^{4}$

$\rm = 1000\times \bigg( \dfrac{105}{100}\bigg)^{4}$

$\rm = 1000\times \bigg( \dfrac{21}{20}\bigg)^{4}$

$\rm = 1000 \times \dfrac{21 \times 21 \times 21 \times 21}{20\times 20 \times 20 \times 20}$

$\rm = 1000 \times \dfrac{194481}{160000}$

$\rm = 1215.50$

$\rm \implies \underline{ \: \: \underline{ \: \: Amount = Rs.1215.50 \: \: } \: \: }$

Now:-

Compound Interest = Amount - Principal

= 1215.50 - 1000

= 215.50

$\underline{\boxed{\purple{\rm \therefore Compound \: Interest = Rs. 215.50}}}$