Question

The compound interest on a certain sum of money for 2 years is Rs. 208 and the simple interest for the same time at the same rate is Rs. 200. Find the rate %.

Answer 1

Step-by-step explanation:

si=p×r×t/100

200=208×r×2/100

5000=104×r

5000/104=r

625/13 =r

Answer 2

The rate is 8%.

Explanation:

Formula for compound interest and simple interest:-

$CI=P((1+r)^t-1)$

$SI=Prt$

, where P= Principal amount , r= rate of interest ( in decimal) and t is time.

As per given , we have

SI = Rs. 200

t= 2

Then,

$200=Pr(2)\\\Rightarrow\ P=\dfrac{200}{2r}=\dfrac{100}{r}$             (1)

Also, CI = Rs. 208

Then, $208=P((1+r)^2-1)$

Put value of P from (1), we get

$208=\dfrac{100}{r}(1+r^2+2r-1)[\because\ (a+b)^2=a^2+b^2+2ab]$

$\dfrac{208}{100}=\dfrac{1}{r}(r^2+2r)=\dfrac{1}{r}(r(r+2))\\\\ 2.08=r+2\\\\ r=2.08-2=0.08$

In percent ,$r=0.08\times100=8\%$

Hence, the rate is 8%.

# Learn more :

Rohit invested some amount at the rate of 6 pcpa and at the end of 3 years he got Rs.8730

simple interest. How much compound interest he will get on same amount and same rate of

interest after 2 years?

a) Rs.5820 b) Rs.5949.60 c) Rs.5900

d) Rs.5994.60 e) None of these

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