The present value of annuity of INR. 5,000 per annum for 12 years at 4% p.a C.I. annually is
Question
The present value of annuity of INR. 5,000 per annum for 12 years at 4% p.a C.I. annually is
Solution
To calculate the present value of an annuity, we use the formula:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
- PV is the present value
- PMT is the annual payment (annuity)
- r is the interest rate
- n is the number of periods
In this case:
- PMT = INR 5,000
- r = 4% or 0.04
- n = 12 years
Substituting these values into the formula, we get:
PV = 5000 * [(1 - (1 + 0.04)^-12) / 0.04]
Now, calculate the expression in the brackets:
= 5000 * [(1 - (1.04)^-12) / 0.04]
= 5000 * [(1 - 0.5523) / 0.04]
= 5000 * [0.4477 / 0.04]
= 5000 * 11.1925
Finally, calculate the present value:
PV = INR 55,962.50
So, the present value of an annuity of INR 5,000 per annum for 12 years at 4% p.a C.I. annually is approximately INR 55,962.50.
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