Annuity Present Value Calculation

What is the present value of an annuity with 30 payments and an interest rate of 20% if the first payment is $5 in year 1?

The present value of the annuity at time zero is $77.22 (Option a).

An annuity represents a series of equal payments made at regular intervals over a specified period. In this case, we are dealing with an annuity consisting of 30 payments with an interest rate of 20%. The present value of the annuity is the current worth of all these future cash flows, discounted at the given interest rate.

To calculate the present value of this annuity, we use the formula for the present value of an ordinary annuity:

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

Where PV is the present value, C is the payment amount, r is the interest rate per period, and n is the number of periods. Plugging in the given values:

PV = $5 * [1 - (1 + 0.20)^-30] / 0.20

= $5 * [1 - 1.376 - 1.376^2 - ... - 1.376^29] / 0.20

≈ $77.22

Therefore, the correct answer is option a, $77.22. This value represents the present worth of all the future payments of the annuity at an interest rate of 20% at the present time.

Understanding present value is crucial in financial planning and investment decisions. By knowing the present value of future cash flows, individuals and businesses can make informed choices regarding investments, loans, and other financial commitments.