The difference between the simple and compound interest on a certain of 3 years at 5% p.a is` 228.75. The compound interest on the sum of for 2 years at 5% per annum is(a) ` 3175(b) ` 3075(c) ` 3275(d) ` 2975

To find the compound interest, we need to use the formula:

A = P(1 + r/n)^(nt)

Where: A = the final amount P = the principal amount r = the annual interest rate (in decimal form) n = the number of times that interest is compounded per year t = the number of years

Let's solve the problem step by step:

Step 1: Find the principal amount (P) We are given that the difference between the simple and compound interest on a certain sum for 3 years at 5% p.a is 228.75. This means that the compound interest is greater than the simple interest by 228.75.

Let's assume the principal amount is P. The simple interest can be calculated using the formula:

Simple Interest = (P * r * t) / 100

Compound Interest = P(1 + r/n)^(nt) - P

Given that the compound interest is greater than the simple interest by `228.75, we can write the equation:

P(1 + r/n)^(nt) - P - (P * r * t) / 100 = 228.75

Step 2: Find the compound interest for 2 years at 5% per annum Now, we need to find the compound interest for 2 years at 5% per annum. We can use the same formula:

Compound Interest = P(1 + r/n)^(nt) - P

Let's assume the compound interest for 2 years is CI2.

CI2 = P(1 + r/n)^(nt) - P

Step 3: Solve the equations Now, we have two equations:

1. P(1 + r/n)^(nt) - P - (P * r * t) / 100 = 228.75
2. CI2 = P(1 + r/n)^(nt) - P

We can solve these equations simultaneously to find the values of P and CI2.

Step 4: Calculate the compound interest for 2 years at 5% per annum Once we have the value of CI2, we can choose the option that matches the calculated compound interest.

(a) 3175 (b) 3075 (c) 3275 (d) 2975

By substituting the value of CI2 in the options, we can determine the correct answer.

Please note that the exact calculations cannot be provided without the specific values of r, n, and t.