Mathematics for FinanceMTP May 18Question 1270 of 512
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A sum of money doubles itself at compound interest in 10\displaystyle 10 years. In how many years will it become eight times

Options

A10\displaystyle 10
B30\displaystyle 30
C40\displaystyle 40
D35\displaystyle 35
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Correct Answer

✅ Option b — 30\displaystyle 30

All Options:

  • A10\displaystyle 10
  • B30\displaystyle 30
  • C40\displaystyle 40
  • D35\displaystyle 35

Detailed Solution & Explanation

**Derivation of Compounding Period** Given: - A sum of money doubles itself (A=2P\displaystyle A = 2P) in 10\displaystyle 10 years under Compound Interest. (1+r)10=2(1 + r)^{10} = 2 **Step 1: Set up the equation for the sum to become 8 times itself (A=8P\displaystyle A = 8P)** (1+r)t=8(1 + r)^t = 8 **Step 2: Express 8 as a power of 2** 8=238 = 2^3 **Step 3: Substitute 2=(1+r)10\displaystyle 2 = (1 + r)^{10}** (1+r)t=[(1+r)10]3(1 + r)^t = \left[(1 + r)^{10}\right]^3 (1+r)t=(1+r)30  ⟹  t=30 years(1 + r)^t = (1 + r)^{30} \implies t = 30 \text{ years} Hence, **Option B** 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.

More Questions from Mathematics for Finance

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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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