Multiple choice

Find the present value of Rs. 500 due in 10 years when interest of 10% is compounded half yearly.

  1. Rs. 188.44

  2. Rs. 193.94

  3. Rs. 138.94

  4. Rs. 50.00
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A Correct answer
Explanation

Present value = A / (1 + r/n)^(nt). Here, A = 500, r = 0.10, n = 2 (half-yearly), t = 10. PV = 500 / (1 + 0.05)^20 = 500 / (1.05)^20. 1.05^20 is approximately 2.653. 500 / 2.653 is approximately 188.44.

AI explanation

Using the present value formula for compound interest, PV equals Amount divided by (1 plus R divided by 100) raised to the power of n. The interest is 10 percent per annum compounded half yearly, so the rate per period is 5 percent and the number of periods in 10 years is 20. Calculating 500 divided by (1 plus 0.05) raised to the power of 20 gives 500 divided by 2.6532, which results in Rs. 188.44.

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