Simple interest is always on the original sum; compound interest is on the sum as it stands. That single sentence generates both formulas and every question that contrasts them.
Questions very often give you the difference between the two over two or three years and ask for the principal, so the two short formulas for that difference are worth memorising outright.
Try each one before opening the answer. A solution you have read is not a solution you can produce under time pressure, which is the only kind that counts.
Q1 Find the compound interest on 8000 at 10% a year for 2 years.
1680.
Amount = 8000 × 1.1² = 8000 × 1.21 = 9680, so the interest is 1680. Simple interest would have been 1600; the extra 80 is the second year’s interest on the first year’s 800.
Q2 The difference between compound and simple interest on a sum at 10% for 2 years is 50. What is the sum?
5000.
The two-year difference is P(R/100)² = P × 0.01. Setting that to 50 gives P = 5000. Checking: SI = 1000, CI = 5000 × 1.21 − 5000 = 1050, and the difference is 50.
Q3 What is the amount on 10,000 at 20% a year for 1 year, compounded half-yearly?
12,100.
Half-yearly means 10% applied twice: 10000 × 1.1² = 12,100. Compounded yearly it would have been 12,000, so the extra compounding is worth 100.