Hemant invested Rs. ‘y’ at the rate of (r+2)% per annum on simple interest and after four years Rs. 27520 was obtained as an interest. If Rs. (y+2500) was invested at the rate of ‘r’% per annum compounded annually and after two years Rs. 16560 was obtained as an interest, then find out the value of ‘r’.

Solution

Hemant invested Rs. ‘y’ at the rate of (r+2)% per annum on simple interest and after four years Rs. 27520 was obtained as an interest.

y x (r+2)% x 4 = 27520

y x (r+2) x 4 = 2752000

y x (r+2) = 688000

y = 688000/(r+2)    Eq.(i)

If Rs. (y+2500) was invested at the rate of ‘r’% per annum compounded annually and after two years Rs. 16560 was obtained as an interest.

(y+2500)[{(100+r)/100}^2 - 1] = 16560 

Put Eq.(i) in the above equation.

(688000/(r+2)+2500)[{(100+r)/100}^2 - 1] = 16560 

5r^3+2386r^2−54000r−662400=0

(r−30) (5r^2+2536r+22080)=0

There are three values of ‘r’. But two of them are negative and not possible.

So the value of ‘r’ = 30.