Question: Sita deposited Rs. 5000 at 10% simple interest for 2 yr. How much more money will Sita have in her account at the end of 2 yr, if it is compounded semi-annually?
Options:
A) Rs. 50
B) Rs. 40
C) Rs. 77.50
D) Rs. 85.50
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, for simple interest
Rate = 10%, Time = 2yr,
Principal = 5000
We know that,
$ Simpleinterest=\frac{Principal\times Rate\times Time}{100} $
$ \Rightarrow $ $ SI=\frac{5000\times 10\times 2}{100}=Rs\text{.}1000 $
(i)
and for compound interest,
Rate = 10% yearly or 5% half-yearly
Time = 2 yr or 4 half years
P = Rs. 5000
When the interest is compounded half-yearly, then the rate of interest is halved because it is compounded twice a year and time taken becomes twice of the original time.
We know that,
$ CI=P[ {{( 1+\frac{r}{100} )}^{t}}-1 ]=5000[ {{( 1+\frac{5}{100} )}^{4}}-1 ] $
$ \Rightarrow $ $ CI=5000[ \frac{194481}{160000}-1 ] $
$ \Rightarrow $ $ CI=\frac{5000\times 34481}{160000}=Rs.1077.5 $ …(ii)
$ \therefore $ Required difference $ =CI-SI $
$ =1077.5-1000=Rs.77.5 $
BETA
