Deepak invested rs 4800 into two schemes a and b at same rate of inter...
Solution:
Given,
Investment in scheme A = Investment in scheme B = Rs 4800
Compound Interest obtained from scheme A in 2 years = Simple Interest obtained from scheme B in 4 years + Rs 50
Let us assume the rate of interest for both schemes A and B to be ‘r’.
Compound Interest for Scheme A:
Principal = Rs 4800, Time = 2 years, Rate = r
CI = P(1 + r/100)^n - P
CI = 4800(1 + r/100)^2 - 4800
Simple Interest for Scheme B:
Principal = Rs 4800, Time = 4 years, Rate = r
SI = (P*r*t)/100
SI = (4800*r*4)/100
According to the question,
CI from scheme A - SI from scheme B = 50
Therefore,
4800(1 + r/100)^2 - 4800 - (4800*r*4)/100 = 50
On solving the above equation, we get r = 5%
Now, if Deepak invested the total sum of Rs 4800 in simple interest for 8 years at the same rate of interest, then the interest obtained becomes equal to the investment.
Simple Interest for 8 years with a rate of interest of 5%:
Principal = Rs 4800, Time = 8 years, Rate = 5%
SI = (P*r*t)/100
SI = (4800*5*8)/100
SI = Rs 1920
Let us assume Deepak invested ‘x’ in scheme B. Therefore, he invested ‘4800-x’ in scheme A.
Share in Scheme B:
Principal = x, Time = 8 years, Rate = 5%
SI = (P*r*t)/100
SI = (x*5*8)/100
SI = 0.4x
Now, we know that the total interest obtained is Rs 1920.
Therefore,
0.4x + 4800 - x = 1920
0.6x = 2880
x = 4800/3
Hence, Deepak invested Rs 1600 in scheme B and Rs 3200 in scheme A.