Q.A sum of ₹10,000 is invested at 10% p.a. compound interest. Using the GP concept, find the amount at the end of 3 years.

Year-end compound-interest amounts form a GP with first term equal to the principal and common ratio $(1+i)$, so the amount after 3 years is simply the corresponding GP term.

Given: Principal $A_0 = ₹10{,}000$, rate $i = 10\% = 0.10$ per annum, $n = 3$ years.

Step 1 — Recognise the GP: successive year-end amounts are $10000,\ 10000(1.1),\ 10000(1.1)^2,\ 10000(1.1)^3, \ldots$ — a GP with $a = 10000$ and $r = 1.10$.

Step 2 — Apply the formula: amount after $n$ years is $A_n = A_0(1+i)^n = 10000 \times (1.10)^3$.

Step 3 — Compute $(1.10)^3$: $(1.10)^2 = 1.21$; $(1.10)^3 = 1.21 \times 1.10 = 1.331$.

Step 4 — Multiply: $A_3 = 10000 \times 1.331 = 13310$. …

Confusing compound interest with simple interest — under simple interest the amount would grow by a constant addition each year (an Arithmetic Progression), not a constant multi …