Economics Time Value Of Money Questions Long
The formula for calculating the present value of an annuity due payment is as follows:
PV = Pmt * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value of the annuity due payment
Pmt = Payment amount received at the beginning of each period
r = Interest rate per period
n = Number of periods
In an annuity due, the payment is received at the beginning of each period, as opposed to the end of each period in a regular annuity. This means that the first payment is received immediately, and subsequent payments are received at the beginning of each period.
The formula takes into account the time value of money, which states that a dollar received in the future is worth less than a dollar received today. By discounting the future cash flows, we can determine the present value of the annuity due payment.
The formula calculates the present value by dividing the payment amount by the interest rate per period and then subtracting the present value of the future cash flows. The present value of the future cash flows is calculated by raising (1 + r) to the power of the number of periods and subtracting it from 1. Finally, the result is divided by the interest rate per period to obtain the present value of the annuity due payment.
It is important to note that the interest rate per period and the number of periods should be consistent. If the interest rate is an annual rate, the number of periods should be in years. If the interest rate is a monthly rate, the number of periods should be in months.