You expect to receive payments of $1,000 at the end of the next three years with an annual interest rate of 5%. How much is the money worth today?
To determine the present value of the future payments, we need to discount them to account for the time value of money. The formula to calculate the present value is as follows:
Present Value = Future Value / (1 + r)^n
Where:
- Future Value is the amount of money you expect to receive in the future
- r is the discount rate (interest rate)
- n is the number of periods (in this case, years)
Let's apply this formula to the given scenario:
Future Value = $1,000 (expected payment)
Interest Rate (r) = 5% (annual interest rate, expressed as a decimal: 0.05)
Number of periods (n) = 3 (three years)
Substituting the values into the formula:
Present Value = $1,000 / (1 + 0.05)^3
Calculating the denominator:
(1 + 0.05)^3 = (1.05)^3 = 1.157625
Substituting the denominator value into the formula:
Present Value = $1,000 / 1.157625
Calculating the present value:
Present Value = $865.12 (rounded to the nearest cent)
Therefore, the money is worth approximately $865.12 today.