Mathematics for FinancePYQ Dec 22Question 1236 of 512
All Questions

If 64\displaystyle 64 amount to 83.20\displaystyle 83.20 in 2\displaystyle 2 years, what will 86\displaystyle 86 amount to in 4\displaystyle 4 years at the same Rate percent per annum?

Options

A127.60\displaystyle 127.60
B147.60\displaystyle 147.60
C145.34\displaystyle 145.34
D117.60\displaystyle 117.60
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Correct Answer

✅ Option c — 145.34\displaystyle 145.34

All Options:

  • A127.60\displaystyle 127.60
  • B147.60\displaystyle 147.60
  • C145.34\displaystyle 145.34
  • D117.60\displaystyle 117.60

Detailed Solution & Explanation

**Derivation of Future Amount under Compound Interest** Given: - Principal 1 (P1\displaystyle P_1) = Rs. 64\displaystyle \text{Rs. }64 - Amount 1 (A1\displaystyle A_1) = Rs. 83.20\displaystyle \text{Rs. }83.20 - Time 1 (t1\displaystyle t_1) = 2\displaystyle 2 years **Step 1: Determine the rate of interest using compounding** A1=P1(1+r)t1A_1 = P_1(1 + r)^{t_1} 83.20=64(1+r)283.20 = 64(1 + r)^2 83.2064=(1+r)2\frac{83.20}{64} = (1 + r)^2 1.30=(1+r)21.30 = (1 + r)^2 **Step 2: Calculate the future amount (A2\displaystyle A_2) of Rs. 86 in 4\displaystyle 4 years (t2=4\displaystyle t_2 = 4)** A2=P2(1+r)t2A_2 = P_2(1 + r)^{t_2} A2=86(1+r)4A_2 = 86(1 + r)^4 A2=86[(1+r)2]2A_2 = 86 \left[(1 + r)^2\right]^2 Using the value (1+r)2=1.30\displaystyle (1+r)^2 = 1.30: A2=86(1.30)2A_2 = 86(1.30)^2 A2=86×1.69=Rs. 145.34A_2 = 86 \times 1.69 = \text{Rs. }145.34 Hence, **Option C** is the correct answer.

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