Mathematics for FinanceMTP May 19 Series IIQuestion 1500 of 512
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5000\displaystyle 5000 paid for ten years to off a loan. What is the loan amount if interest rate be 14%\displaystyle 14\% per annum compounded annually? [Given P(10,0.14)=5.2161]\displaystyle [Given \ P(10, 0.14) = 5.2161]

Options

A26085.50\displaystyle 26085.50
B26080.55\displaystyle 26080.55
C26280.55\displaystyle 26280.55
D27080.55\displaystyle 27080.55
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Correct Answer

✅ Option a — 26085.50\displaystyle 26085.50

All Options:

  • A26085.50\displaystyle 26085.50
  • B26080.55\displaystyle 26080.55
  • C26280.55\displaystyle 26280.55
  • D27080.55\displaystyle 27080.55

Detailed Solution & Explanation

The loan amount (PV\displaystyle PV) is: PV=A×P(10,0.14)PV = A \times P(10, 0.14) Given: * Annual payment (A\displaystyle A) = 5,000\displaystyle 5,000 * Factor P(10,0.14)=5.2161\displaystyle P(10, 0.14) = 5.2161 Substituting the values: PV=5,000×5.2161=26,080.50PV = 5,000 \times 5.2161 = 26,080.50 This is closest to Option A (26,085.50\displaystyle 26,085.50). Hence, **Option A** is the correct answer.

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