Final answer:
The question involves mathematics, specifically financial mathematics concerning present value and future value calculations using a 15% interest rate. Present value calculation assesses what a future sum of money is worth currently, while future value projections determine what a current amount will be valued at in the future.
Step-by-step explanation:
Understanding Present Value and Future Value Calculations
The present value calculation is a financial concept used to determine the current worth of an amount that will be received in the future, taking into account a specific interest rate. For instance, receiving a lump sum payment of $1350 in four years would have a different present value if the interest rate is 15%. To calculate this, we use the formula:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value ($1350), r is the interest rate (expressed as a decimal), and n is the number of periods (years in this case).
Similarly, future value calculations are used to find out how much a current amount will be worth in the future, having been invested at a certain interest rate over a period of time. This concept is crucial for making informed decisions on investments or savings. To calculate future value, the formula used is:
FV = PV * (1 + r)^n
Both calculations are essential in finance for assessing the time value of money, which is the idea that money available now is worth more than the identical sum in the future due to its potential earning capacity.
For loans, similar calculations apply where the present value is what is borrowed and the future value is the repayment, which includes interest over the time.