What amount must be set aside now to generate payments of $30,000 at the beginning of each year for the next 13 years if money is worth 5.93%, compounded annually? (Round your answer to the nearest cent.)
PV = 30,000 + 30,000( 1 - 1.0593^-12)/.0593
= ....
To determine the amount that must be set aside now to generate future payments, we can use the concept of present value. Present value calculations allow us to find the current worth of a future cash flow, taking into consideration the time value of money and the interest rate.
In this case, we need to find the present value of a stream of payments. The formula to calculate the present value of an annuity is:
PV = PMT × [1 - (1 + r)^(-n)] / r
Where:
PV = Present Value (the amount to be set aside now)
PMT = Payment amount ($30,000 in this case)
r = Interest rate per period (5.93% or 0.0593 in decimal form)
n = Number of periods (13 years)
Let's plug in the values and calculate the present value:
PV = $30,000 × [1 - (1 + 0.0593)^(-13)] / 0.0593
Using a calculator to evaluate the expression inside the brackets:
PV = $30,000 × [1 - 0.278261142] / 0.0593
PV = $30,000 × 0.721738858 / 0.0593
Multiplying the two values together:
PV = $43324.17
Therefore, approximately $43,324.17 must be set aside now to generate payments of $30,000 at the beginning of each year for the next 13 years, given an interest rate of 5.93% compounded annually.