The interest received on a sum of money when invested in scheme A is equal to the interest received on the same sum of money when invested for 2 years in scheme B. Scheme A offers simple interst (p.c.p.a) and Scheme B offers compound interest (compounded annually). Both the scheme offers the same rate of interest. If the numerical value of the number of years for which the sum is invested in Scheme A is same as the numerical value of the rate of interest offered by the same scheme, what is the rate of interest (p.c.p.a) offered by scheme A
Let the rate of interest be r.
According to question,
P×r×r/100 = P[(1+r/100)2-1]
⇒ r2/100 =1+r2/10000+2r/100-1
⇒ r2/100 =r2/10000+r/50
⇒r/100=r/10000+r/50
⇒r/100-r/10000=1/50
⇒99r/10000=1/50
99r = 200
r = 200/99 = 2 2/99%
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