Question

The simple interest on a sum of money for 2 years at 8% per annum is Rs 640. What
will be the compound interest on the same sum at the same rate for the same period,
compounded annually?

Answer 1

SI for 2 years = 640 Rs.
SI is constant each year(for the same rate)
Hence SI for 1 year= 640/2 = 320.
Now CI for 1st year and SI for 1st year are the same.
Hence CI for 1st year= 320 Rs.
CI for 2nd year = SI + R*SI/100 = 320 + 8*320/100 = 320 + 25.6 = 345.6Rs.
Hence CI for 2 years= 320+345.6 = Rs. 665.6
                      OR
SI = P*R*T/100
640= P*8*2/100
P = 640*100/8*2 = Rs.4000
Now, CI = P[ (1+r/100)^n -1]
CI = 4000* [ (1 + 8/100)^2 - 1]
     = 4000* [ (108/100)^2 - 1] = 4000* [(27/25)^2 - 1]
     = 4000*[ (729-625)/625]
     == 4000*104/625 = Rs.665.6