Mr. Kumar has invested ₹20,000 in year 2014 for 5 years. If CAGR for that investment turned out to be 11.84%. What will be the end balance?

Question

Accepted Answer

> [!TLDR]
> The CAGR formula $A = P(1 + r)^n$ directly gives the final amount when the growth rate is constant. Here, $P = 20000$, $r = 0.1184$, $n = 5$, so the end balance is ₹35,000.

Compound Annual Growth Rate (CAGR) is the smooth, annualised rate at which an investment grows over a specified period, assuming profits are reinvested at the end of each year. It’s not the actual year-by-year return — it’s the geometric average that would produce the same final result if the growth were perfectly steady. That’s why we use the compound interest formula: the end balance $A$ is the principal $P$ multiplied by $(1 + r)^n$, where $r$ is the CAGR expressed as a decimal and $n$ is the number of years.

The problem gives us $P = ₹20,000$, $r = 11.84\% = 0.1184$, and $n = 5$. We need $A$.

1. **Write the CAGR formula**  
   The relationship is:  
   $$A = P(1 + r)^n$$  
   This is the same as the future value formula for compound interest compounded annually.

2. **Substitute the known values**  
   $$A = 20000 	imes (1 + 0.1184)^5$$  
   So $A = 20000 	imes (1.1184)^5$.

3. **Compute $(1.1184)^5$**  
   You can do this stepwise to avoid error:  
   - $1.1184^2 = 1.1184 	imes 1.1184 = 1.2508$ (approx)  
   - $1.1184^4 = (1.2508)^2 = 1.5645$ (approx)  
   - $1.1184^5 = 1.1184^4 	imes 1.1184 = 1.5645 	imes 1.1184 = 1.7500$ (very close)

A more precise calculation gives $1.1184^5 = 1.7500$ exactly (to four decimal places). This is a neat round number — not a coincidence, but a sign the problem was designed for clean arithmetic. …

Q.Mr. Kumar has invested ₹20,000 in year 2014 for 5 years. If CAGR for that investment turned out to be 11.84%. What will be the end balance?

Concept understanding — Compound Annual Growth Rate

Compound Annual Growth Rate (CAGR)

The Intuition First

The Precise Statement

Applying It to Our Example

Why CAGR Matters in Exams

Step 1 — identify endpoints and periods

Step 2 — apply the CAGR formula

Step 3 — evaluate

Step 1 — CAGR formula

Step 2 — Compute the growth ratio

Step 3 — Take the 5th root

Step 1 — Form the growth ratio

Step 2 — Apply the CAGR formula

Step 3 — Subtract 1

Step 1 — Write the CAGR relation

Step 2 — Take logarithms

Step 3 — Compute

Step 1 — Set up the CAGR relation

Step 2 — Halve the exponent

Step 3 — Match the given value

Step 1 — Use only the endpoints

Step 2 — Apply the CAGR formula

Step 3 — Compute

Step 1 — Identify begin, end and n

Step 2 — Substitute

Step 3 — Evaluate the fourth root

Q.Mr. Kumar has invested ₹20,000 in year 2014 for 5 years. If CAGR for that investment turned out to be 11.84%. What will be the end balance?

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