An amount of Rs. ‘y’ was invested on (R-2)% per annum on simple interest and at the end of 6 years an amount of Rs. 23100 was obtained as an interest. If the amount was Rs. 7000 more and the rate of interest was ‘R’% per annum on simple interest, then at the end of 4 years an amount of Rs. 22320 was obtained as an interest. Find out the compound interest obtained on Rs. (y-5000) at the rate of (R+1)% per annum compounded annually for the period of 2 years. The value of ‘R’ is a natural number.

Solution

An amount of Rs. ‘y’ was invested on (R-2)% per annum on simple interest and at the end of 6 years an amount of Rs. 23100 was obtained as an interest.

y x (R-2)% x 6 = 23100

y x (R-2) = 385000

y = 385000/(R-2)    Eq.(i)

If the amount was Rs. 7000 more and the rate of interest was ‘R’% per annum on simple interest, then at the end of 4 years an amount of Rs. 22320 was obtained as an interest.

(y+7000) x R% x 4 = 22320

(y+7000) x R = 558000    Eq.(ii)

Put Eq.(i) in Eq.(ii).

[{385000/(R-2)}+7000] x R = 558000

After solving the above equation, R  = 9 .

Put the value of ‘R’ in Eq.(i).

y = 385000/(9-2)

= 385000/7

y = 55000

Required compound interest = (y-5000) of (100+R+1)% of (100+R+1)% - (y-5000)

Put the values of ‘y’ and ‘R in the above equation.

= (55000-5000) of (100+9+1)% of (100+9+1)% - (55000-5000)

= 50000 of 110% of 110% - 50000

= 60500 - 50000

= Rs. 10500