Mr. X makes a deposit of 12,000 in a bank where the amount doubles at compound interest in 5 years, then what will be the total amount he will have after twenty years?

Option d: 1,92,000. Solution: Derivation of Future Value Given: - Principal (P) = text{Rs. }12,000 - The money doubles at compound interest every 5 years. Step 1: Set up the doubling formula Let t be the total time and d = 5 years be the doubling period. The future value A after t years is: A = P x 2^{t/d} Step 2: Calculate the amount after 20 years (t = 20) A = 12000 x 2^{20/5} A = 12000 x 2^4 A = 12000 x 16 = text{Rs. }1,92,000 Hence, Option D is the correct answer.

Mr. X makes a deposit of $12,000$ in a bank where the amount doubles at compound interest in $5$ years, then what will be the total amount he will have after twenty years?

The correct answer is Option d: $1,92,000$. **Derivation of Future Value** Given: - Principal ($P$) = $\text{Rs. }12,000$ - The money doubles at compound interest every $5$ years. **Step 1: Set up the doubling formula** Let $t$ be the total time and $d = 5$ years be the doubling period. The future value $A$ after $t$ years is: $$A = P \times 2^{t/d}$$ **Step 2: Calculate the amount after 20 years ($t = 20$)** $$A = 12000 \times 2^{20/5}$$ $$A = 12000 \times 2^4$$ $$A = 12000 \times 16 = \text{Rs. }1,92,000$$ Hence, **Option D** is the correct answer.

Mathematics for FinancePYQ Sep 24Question 1269 of 512

All Questions

Mr. X makes a deposit of $\displaystyle 12,000$ in a bank where the amount doubles at compound interest in $\displaystyle 5$ years, then what will be the total amount he will have after twenty years?

Options

\displaystyle 1,20,000

\displaystyle 96,000

\displaystyle 1,24,000

\displaystyle 1,92,000

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — $\displaystyle 1,92,000$

All Options:

A $\displaystyle 1,20,000$
B $\displaystyle 96,000$
C $\displaystyle 1,24,000$
D $\displaystyle 1,92,000$

Detailed Solution & Explanation

**Derivation of Future Value** Given: - Principal (

\displaystyle P

) =

\displaystyle \text{Rs. }12,000

- The money doubles at compound interest every

\displaystyle 5

years. **Step 1: Set up the doubling formula** Let

\displaystyle t

be the total time and

\displaystyle d = 5

years be the doubling period. The future value

\displaystyle A

after

\displaystyle t

years is:

A = P \times 2^{t/d}

**Step 2: Calculate the amount after 20 years (

\displaystyle t = 20

)**

A = 12000 \times 2^{20/5}

A = 12000 \times 2^4

A = 12000 \times 16 = \text{Rs. }1,92,000

Hence, **Option D** is the correct answer.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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Mr. X makes a deposit of 12,000\displaystyle 12,00012,000 in a bank where the amount doubles at compound interest in 5\displaystyle 55 years, then what will be the total amount he will have after twenty years?