The value of compound interest (in nearest $₹$) if $₹30,00,000$ is deposited in a bank for 1 year at the rate of 16% per annum compounded quarterly is:
(A) 5,07,575
(B) 5,78,360
(C) 5,09,576
(D) 5,72,540

Question

Accepted Answer

> [!TLDR]
> $A=30{,}00{,}000	imes(1.04)^4=₹35{,}09{,}575.68$, so $CI=A-P\approx₹5{,}09{,}576$.

### Step 1 — Set per-period rate and periods

Nominal 16% compounded quarterly: rate per quarter $i=16\%/4=4\%=0.04$; number of quarters in 1 year $n=4$.

### Step 2 — Amount

$$A=P(1+i)^n=30{,}00{,}000	imes(1.04)^4.$$

$$(1.04)^4=1.16985856,$$

so

$$A=30{,}00{,}000	imes1.16985856=₹35{,}09{,}575.68.$$

### Step 3 — Compound interest

$$CI=A-P=35{,}09{,}575.68-30{,}00{,}000=₹5{,}09{,}575.68\approx₹5{,}09{,}576.$$ …

Compound Interest

Compound Annual Growth Rate (CAGR)

The Intuition First

The Precise Statement

Applying It to Our Example

Why CAGR Matters in Exams

Step 1 — Set per-period rate and periods

Step 2 — Amount

Step 3 — Compound interest

Step 1 — Set per-period rate and periods

Step 2 — Amount

Step 3 — Compound interest

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