Mathematics for FinanceMTP May 20Question 1509 of 512
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A person invests 500\displaystyle 500 at the end of each year with a bank which pays interest at 10%\displaystyle 10\% p.a C.I. annually. The amount standing to his credit one year after he has made his yearly investment for the 12th\displaystyle 12^{th} time is, Given (1.1)12=3.1384\displaystyle (1.1)^{12} = 3.1384.

Options

A11,761.36\displaystyle 11,761.36
B10,000\displaystyle 10,000
C12,000\displaystyle 12,000
Dnone of these
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Correct Answer

✅ Option a — 11,761.36\displaystyle 11,761.36

All Options:

  • A11,761.36\displaystyle 11,761.36
  • B10,000\displaystyle 10,000
  • C12,000\displaystyle 12,000
  • Dnone of these

Detailed Solution & Explanation

First, we find the future value of the annuity (FV\displaystyle FV) immediately after the 12th\displaystyle 12^{\text{th}} payment: FV12=A[(1+i)n−1i]FV_{12} = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Annual investment (A\displaystyle A) = 500\displaystyle 500 * Time (n\displaystyle n) = 12\displaystyle 12 years * Interest rate (i\displaystyle i) = 10%\displaystyle 10\% p.a. = 0.10\displaystyle 0.10 * Given factor (1.1)12=3.1384\displaystyle (1.1)^12 = 3.1384 Substituting the values: FV12=500[3.1384−10.10]=500×21.384=10,692FV_{12} = 500 \left[ \frac{3.1384 - 1}{0.10} \right] = 500 \times 21.384 = 10,692 Since we want the value standing to his credit one year after the 12th\displaystyle 12^{\text{th}} investment, we compound it for one more year: FV=10,692×(1+0.10)=11,761.20FV = 10,692 \times (1 + 0.10) = 11,761.20 This is closest to Option A (11,761.36\displaystyle 11,761.36). Hence, **Option A** is the correct answer.

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