Question

The difference between simple interest and compound interest on a sum for 2 years at 8%. when the interest is compounded annually is rs.16 then find the sum.​

Answer 1

Step-by-step explanation:

Here, r = 8, t = 2 and sum be p

Now SI = prt/100 = p.8.2/100 = 4p/25.

CI = A - P

= P(1+r/100)^t - p

= P[(1+8/100)^2 - 1]

= P[(27/25)^2 -1]

= P[729/625 -1]

= p * 104/625

Now, CI - SI = 16

Or, 104p/625 - 4p/25 = 16

Or, 4p/625 = 16

Or, p = 2500

If the interest rate Compounded half yearly, then r = 8/2 = 4 and t = 2*2 = 4, p = 2500

Hence , CI = A -P

Or, p(1+r/100)^t - p

Or, p[(1+4/100)^4 - 1]

Or, 2500[(26/25)^4 -1]

Or, 2500*[(456976/390625) - 1]

Or, 2500*66351/390625

Or, 424.65

SI = 4p/25 = 4*2500/25 = 400

Hence diff between two interests = 424.65 - 400 = 24.65