Present Value of Annuity Calculation

What is the correct present value of an annuity with 10 payments?

Your friend promises you an annuity of 10 payments. If the first payment of $10 occurs in year 1 and the interest rate is 10%, which of the following is right about its present value at time zero?

Correct Answer:

The correct present value of the annuity at time zero is $15.92.

In finance, the present value of an annuity is a crucial concept used to determine the current worth of a series of future cash flows, taking into account the time value of money. In this scenario, we are dealing with an annuity of 10 payments with the first payment of $10 occurring in year 1 and an interest rate of 10%.

To calculate the present value of the annuity at time zero, we first calculate the present value of each payment using the formula for the present value of an ordinary annuity:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where:

PV = Present Value

PMT = Payment per period

r = Interest rate

n = Number of periods

Given that PMT is $10, r is 10%, and n is 10, we can plug these values into the formula:

PV = 10 * (1 - (1 + 0.10)^(-10)) / 0.10

= 10 * (1 - 0.3855) / 0.10

= 10 * 0.6145

= $6.145

However, to find the present value at time zero, we need to multiply this value by (1 + r)^(n-1) to adjust for the time value of money:

PV at time zero = $6.145 * (1 + 0.10)^(10-1)

= $6.145 * 1.1^9

= $6.145 * 2.5937

= $15.92

Therefore, the correct present value of the annuity at time zero is $15.92, which is not one of the listed answer options. This calculation underscores the importance of understanding present value concepts in financial analysis and decision-making.