Question

Find the amount and the compound interest on 10,000 for 1 1/2 years at 10% per
annum, compounded half yearly. Would this interest be more than the interest he
would get if it was compounded annually?​

Answer 1

Step-by-step explanation:

Principal = Rs.10,000

Time =   $1\frac{1}{2}$ years

Rate = 10% per annum

CASE 1 Interest on compounded half yearly.

Rate = 10% per annum  = 5 % per half yearly

T= $1\frac{1}{2} years,n=3$

A= $P\left ( 1+\frac{R}{100} \right )^{n}$

A= $10000\left ( 1+\frac{5}{100} \right )^{3}$

A= $10000\left ( 1+0.05 \right )^{3}$

A=$10000\left ( 1.05 \right )^{3}$

A= 11576.25 = Amount

CI = Amount - principal

CI  = 11576.25-10000

CI = 1576.25

CASE 2    Interest on compounded annually

Rate = 10% per annum

 T= $1\frac{1}{2} years ,n=1$

A= $P\left ( 1+\frac{R}{100} \right )^{n}$

A= $10000\left ( 1+\frac{10}{100} \right )^{1}$

A= $10000\left ( 1+0.1\right )^{1}$

A= $10000\left ( 1.1\right )^{1}$

A= 11000 = Amount

CI = Amount - principal

CI  = 11000-10000  

CI = 1000

Interest for half years on 11000 =  

$\frac{P\times R\times T}{100}$

$=\frac{11000\times 10\times \frac{1}{2}}{100}$

= 55\times 10  

= 550  

Total interest = 1000+550  = Rs. 1550

Since 1576.25 > 1000

Thus, interest would be more in CASE 1 i.e. compounded half yearly

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