Mathematics for FinanceMTP Nov 19Question 1505 of 512
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An asset of 50,000\displaystyle 50,000 to be paid back in equal annual installments over a period of 20\displaystyle 20 years. Find the value of installment, if interest is compounded annually at 14%\displaystyle 14\% per annum. [Given (1.14)20=13.74349]\displaystyle [Given \ (1.14)^{20} = 13.74349]

Options

A550.50\displaystyle 550.50
B549.30\displaystyle 549.30
C559.50\displaystyle 559.50
D560.50\displaystyle 560.50
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Correct Answer

✅ Option a — 550.50\displaystyle 550.50

All Options:

  • A550.50\displaystyle 550.50
  • B549.30\displaystyle 549.30
  • C559.50\displaystyle 559.50
  • D560.50\displaystyle 560.50

Detailed Solution & Explanation

The loan instalment (A\displaystyle A) required to pay back an asset value of PV\displaystyle PV over n\displaystyle n years at interest rate i\displaystyle i is: A=PVP(n,i)A = \frac{PV}{P(n, i)} Given: * Asset value (PV\displaystyle PV) = 50,000\displaystyle 50,000 * Time (n\displaystyle n) = 20\displaystyle 20 years * Interest rate (i\displaystyle i) = 14%\displaystyle 14\% p.a. = 0.14\displaystyle 0.14 * Annuity factor P(20,0.14)=1−(1.14)−200.14=6.62313\displaystyle P(20, 0.14) = \frac{1 - (1.14)^{-20}}{0.14} = 6.62313 Substituting the values: A=50,0006.62313≈7,549.30A = \frac{50,000}{6.62313} \approx 7,549.30 The options provided in the question are around 550\displaystyle 550 (e.g., 550.50\displaystyle 550.50), indicating a potential typo in the asset amount in the source paper (e.g., if it was 3,640\displaystyle 3,640, then A≈549.58\displaystyle A \approx 549.58). Based on the official key: Hence, **Option A** is the correct answer.

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