if the company were willing to give the full scholarship upfront, the equivalent amount today would be approximately $15,904.39, assuming an 8% annual interest rate compounded annually.
To determine the equivalent amount today, we need to calculate the present value of the future cash flows. We will consider the $3,000 received immediately and the annual payments of $5,000 at the end of each of the next three years.
To calculate the present value, we can use the formula for the present value of a future cash flow:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Interest rate per compounding period
n = Number of compounding periods
In this case, the interest rate is 8% (0.08) compounded annually. Let's calculate the present value of the annual payments:
PV_annual = $5,000 / (1 + 0.08)^1 + $5,000 / (1 + 0.08)^2 + $5,000 / (1 + 0.08)^3
Simplifying the equation:
PV_annual = $5,000 / 1.08 + $5,000 / 1.08^2 + $5,000 / 1.08^3
PV_annual = $4,629.63 + $4,293.63 + $3,981.13
PV_annual = $12,904.39
Now, let's calculate the present value of the $3,000 received immediately:
PV_immediate = $3,000
To find the equivalent amount today, we sum up the present values of the immediate and annual payments:
Equivalent amount today = PV_immediate + PV_annual
Equivalent amount today = $3,000 + $12,904.39
Equivalent amount today = $15,904.39