Q1.
Suppose we want to know the expression/formula to find the total interest amount gained at the end of the maturity period. What would be the formula for each of the two options?
Answer
Interest is whatever the deposit has gained above the principal, so in both cases subtract p from the maturity amount.
| Amount at maturity | Total interest | |
|---|---|---|
| Without compounding | p(1 + rt) | p(1 + rt) – p = prt |
| With compounding | p(1 + r)t | p(1 + r)t – p = p[(1 + r)t – 1] |
Check with the chapter's numbers — p = 6000, r = 0.1, t = 3
Without compounding: prt = 6000 × 0.1 × 3 = ₹1800 ✓ (7800 – 6000)
With compounding: 6000[(1.1)³ – 1] = 6000 × 0.331 = ₹1986 ✓ (7986 – 6000)
Without compounding: prt = 6000 × 0.1 × 3 = ₹1800 ✓ (7800 – 6000)
With compounding: 6000[(1.1)³ – 1] = 6000 × 0.331 = ₹1986 ✓ (7986 – 6000)
Why it happens: In the first formula the interest prt is a plain product — triple the years and you triple the interest. In the second, the years sit in the exponent, so the interest is p times ((1 + r)ᵗ – 1), and that bracket grows faster than t does. The “– 1” is doing the same job as the “– p” before it was factored out: it removes the original principal, which was never interest.