Suppose your mom decides to gift you ` 10,000 every year starting from today for
the next five years. You deposit this amount in a bank as and when you receive and get 10% per
annum interest rate compounded annually. What is the present value of this annuity?

Question

Answer

Calculating Present Value of Annuity

An annuity is a series of equal payments or receipts made at fixed intervals. In this case, your mother is gifting you ` 10,000 every year for the next five years, which makes it an annuity. The present value of this annuity is the value of all the payments in today's money.

Formula for Present Value of Annuity

The formula to calculate the present value of an annuity is as follows:

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

Where,

PV = Present Value
A = Annual Payment
r = Interest Rate per Annum
n = Number of Years

Calculating Present Value of Annuity in Detail

To calculate the present value of this annuity, we need to follow these steps:

Step 1: Find the annual payment
In this case, the annual payment is ` 10,000.

Step 2: Determine the interest rate
The interest rate is 10% per annum, compounded annually.

Step 3: Determine the number of years
The annuity is for the next five years.

Step 4: Plug the values into the formula
PV = 10,000 * [(1 - (1 + 0.10)^-5) / 0.10]

PV = ` 39,471.69

Therefore, the present value of this annuity is ` 39,471.69.

Conclusion

In conclusion, the present value of an annuity is the current value of a series of future payments, discounted by the interest rate. By using the formula for calculating present value of annuity, we can find out the present value of any annuity. In this case, the present value of the annuity is ` 39,471.69.

Answer

41,699

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