Find the compound interest on Rs. 1000 at the rate of 20% per annum for 18 month when interest is compounded half yearly.
A. Rs. 331
B. Rs. 1331
C. Rs. 320
D. Rs. 325
E. None of these
Answer: Option A
Solution (By Examveda Team)
$$\eqalign{ & {\text{Given,}}\,{\text{Principal}},\,P = Rs.\,1000 \cr & {\text{Compoind}}\,{\text{rate}},\,R = 20\% \,{\text{per}}\,{\text{annum}} \cr & = \frac{{20}}{2} = 10\% \,{\text{half - yearly}} \cr & {\text{Time}} = 18\,{\text{month}} = 3\,{\text{half - years}} \cr & {\text{Amount}}, \cr & A = \left\{ {P \times {{\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right]}^n}} \right\} \cr & = \left\{ {1000 \times {{\left[ {1 + \left( {\frac{{10}}{{100}}} \right)} \right]}^3}} \right\} \cr & = { {\frac{{1000 \times 11 \times 11 \times 11}}{{10 \times 10 \times 10}}} } \cr & A = Rs.\,1331 \cr & {\text{Hence,}}\,{\text{compound}}\,{\text{interest}} = Rs.\,331 \cr} $$This Question Belongs to Arithmetic Ability >> Interest
To find the compound interest, we can use the formula:
CI = P x (1 + r/n)^(nt) - P
Where:
CI = Compound Interest
P = Principal Amount (Rs. 1000)
r = Annual interest rate (20% = 0.20)
n = Number of times interest is compounded per year (2, since it's compounded half-yearly)
t = Time in years (18 months = 1.5 years)
Plugging in the values:
CI = 1000 x (1 + 0.20/2)^(2*1.5) - 1000
CI = 1000 x (1.10)^3 - 1000
CI = 1331 - 1000
CI = Rs. 331
So, the compound interest is Rs. 331.
The total amount after 18 months will be Rs. 1000 + Rs. 331 = Rs. 1331.
could someone tell me how 18months is 3 half years
or any simplr formula??
I have 260
I solved Find the amount and compound interest on rs 16000 for 1.5 years at 10% per annum the interest begin compounded half yearly? and got answer as (Compound interest:rup 38000)
Thanks.
Syed Rashed.
@Nilesh, Interest is compounded half yearly.
And, In half yearly Interest , rate is taken as half of the original rate.
Here, Original rate is 20% but, it is compounded half yearly so it will become half i.e. 10%.
Now, do your calculation, you will get the answer.
A= p ( 1 + r|100)n
A= 1000( 1+ 20| 100) ﾃモﾃつｳ
1000 ( 1.2)ﾃモﾃつｳ
1000 ( 1.728)
1000ﾃャﾃｯﾂｿﾂｽ 1.728
Ans A= 1728
How get the ans 331 plz help me