Mathematics for FinanceMTP May 20Question 1510 of 512
All Questions

The present value of 10,000\displaystyle 10,000 due in 2\displaystyle 2 years at 5%\displaystyle 5\% p.a. compound interest when the interest is paid on half-yearly basis is

Options

A9,070\displaystyle 9,070
B9,070\displaystyle 9,070
C9,060\displaystyle 9,060
Dnone of these
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — 9,060\displaystyle 9,060

All Options:

  • A9,070\displaystyle 9,070
  • B9,070\displaystyle 9,070
  • C9,060\displaystyle 9,060
  • Dnone of these

Detailed Solution & Explanation

The present value (PV\displaystyle PV) of a future sum compounded semi-annually is: PV=FV(1+r2)2nPV = \frac{FV}{\left(1 + \frac{r}{2}\right)^{2n}} Given: * Future Value (FV\displaystyle FV) = 10,000\displaystyle 10,000 * Time (n\displaystyle n) = 2\displaystyle 2 years * Nominal rate (r\displaystyle r) = 5%\displaystyle 5\% p.a. = 0.05\displaystyle 0.05 Substituting the values: PV=10,000(1+0.025)4=10,000(1.025)4=10,0001.103813≈9,059.50≈9,060PV = \frac{10,000}{(1 + 0.025)^4} = \frac{10,000}{(1.025)^4} = \frac{10,000}{1.103813} \approx 9,059.50 \approx 9,060 Hence, **Option C** is the correct answer.

Key Concepts to Understand

More Questions from Mathematics for Finance

Ready to Master Mathematics for Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free