Mathematics for FinanceMTP Jun 23 Series IQuestion 1522 of 512
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10,000\displaystyle 10,000 is invested every month and in an account paying interest @12%\displaystyle @12\% per annum compounded monthly. What is the future value of this annuity just after making 11th\displaystyle 11^{th} payment

Options

A115,600\displaystyle 115,600
B116,100\displaystyle 116,100
C156,800\displaystyle 156,800
D157,100\displaystyle 157,100
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Correct Answer

✅ Option a — 115,600\displaystyle 115,600

All Options:

  • A115,600\displaystyle 115,600
  • B116,100\displaystyle 116,100
  • C156,800\displaystyle 156,800
  • D157,100\displaystyle 157,100

Detailed Solution & Explanation

The future value (FV\displaystyle FV) of an ordinary annuity compounded monthly is: FV=A[(1+i)n−1i]FV = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Monthly investment (A\displaystyle A) = 10,000\displaystyle 10,000 * Number of payments (n\displaystyle n) = 11\displaystyle 11 * Nominal rate = 12%\displaystyle 12\% p.a., so periodic rate i=12%12=1%=0.01\displaystyle i = \frac{12\%}{12} = 1\% = 0.01 Substituting the values: FV=10,000[(1.01)11−10.01]FV = 10,000 \left[ \frac{(1.01)^{11} - 1}{0.01} \right] Using (1.01)11≈1.115668\displaystyle (1.01)^{11} \approx 1.115668: FV=10,000[1.115668−10.01]=10,000×11.5668=1,15,668FV = 10,000 \left[ \frac{1.115668 - 1}{0.01} \right] = 10,000 \times 11.5668 = 1,15,668 This is closest to Option A (115,600\displaystyle 115,600). Hence, **Option A** is the correct answer.

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