I have been promised a $25,000 car when i graduate in four years. If money earns 7% interest, what is my promise worth now?
To calculate the present value of the promised car, we need to account for the time value of money by discounting the future value at the given interest rate. Here are the steps to find out the present value:
1. Determine the number of compounding periods: Since you are given a 7% interest rate, we assume it is compounded annually. As you mentioned that you will graduate in four years, the number of compounding periods is also four.
2. Use the formula for calculating the present value of a future amount: the present value (PV) is equal to the future value (FV) divided by (1 + interest rate)^number of periods.
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Interest Rate
n = Number of Periods
3. Substitute the given values into the formula:
FV = $25,000 (the promised car value)
r = 7% or 0.07 (converted into decimal form)
n = 4 (number of years)
PV = $25,000 / (1 + 0.07)^4
4. Calculate the present value:
PV = $25,000 / (1.07)^4
PV = $25,000 / 1.310796897
5. Round the present value to the nearest dollar:
PV ≈ $19,067.97
Therefore, the present value of the promised $25,000 car, considering a 7% interest rate over four years, is approximately $19,067.97.