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The present value of annuity of INR. 5,000 per annum for 12 years at 4% p.a C.I. annually isa.46,000b.45,850c.15,000d.46925

Question

The present value of annuity of INR. 5,000 per annum for 12 years at 4% p.a C.I. annually isa.46,000b.45,850c.15,000d.46925

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Solution

The present value of an annuity can be calculated using the formula:

PV = P * [(1 - (1 + r)^-n) / r]

where:

  • PV is the present value
  • P is the amount of each annuity payment (in this case, INR 5,000)
  • r is the interest rate per period (in this case, 4% or 0.04)
  • n is the number of periods (in this case, 12 years)

Substituting the given values into the formula, we get:

PV = 5000 * [(1 - (1 + 0.04)^-12) / 0.04]

Solving the equation step by step:

  1. Calculate (1 + r) = (1 + 0.04) = 1.04
  2. Raise the result to the power of -n = 1.04^-12 ≈ 0.66506
  3. Subtract the result from 1 = 1 - 0.66506 = 0.33494
  4. Divide the result by r = 0.33494 / 0.04 = 8.3735
  5. Multiply the result by P = 8.3735 * 5000 = 41,867.5

So, the present value of the annuity is approximately INR 41,867.5. This is not an option in the choices provided, so there may be a mistake in the question or the options.

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