Answers

2014-07-29T15:48:34+05:30
The ratio of the amount for 2 years under compound interest annually and for one year under simple interest is in the ratio 6 is to 5. When the rate of interest is the same then the value of the rate of interest is?

Solution:
Let the Principal be Rs 100
time = 2years
Rate = r

Case i) Amount in compound interest = 
P[1+ \frac{r}{100}]^n\\= [tex]100[1+ \frac{r}{100}]^2

 = 100[\frac{100+r}{100}]^2

[\frac{(100+r)^2}{100}]

Amount in SI =  \frac{PTR}{100} + P

 \frac{100*1*r}{100} + 100 = r +100

Given ratio= 6 : 5

Therefore, \frac{(100+r)^2}{100} : r+100 = 6 : 5

On simplification,

\frac{(100+r)^2}{100} * 5 = 6(r + 100)

\frac{(100+r)^2}{20} = 6r + 600)

10000 + r^2 + 200r = 120r + 12000

 r^2 + 80r - 2000 = 0

(r + 100) (r - 20) = 0

Therefore, r = 20

Rate of interest = 20%



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