Present value,
How do I calculate the present value of:
7,000.00 in 5 years at a quarterly discount rate of 6%?
I have read over the material, but I don't get it.
Thank you
To calculate the present value of a future amount, you need to discount it back to the present using the appropriate discount rate. In this case, the discount rate is given as a quarterly rate of 6%.
Here's how you can calculate the present value of $7,000.00 in 5 years at a quarterly discount rate of 6%:
Step 1: Convert the annual discount rate to a quarterly rate:
Since the discount rate is stated as an annual rate, you need to convert it to a quarterly rate. Divide the annual rate by the number of quarters in a year. In this case, a year has four quarters:
Quarterly rate = Annual rate / Number of quarters per year
Quarterly rate = 6% / 4
Quarterly rate = 1.5%
Step 2: Determine the number of discounting periods:
Since the future amount is given in years, and the discount rate is expressed on a quarterly basis, you need to determine the number of quarters that correspond to 5 years:
Number of quarters = Number of years * Number of quarters per year
Number of quarters = 5 * 4
Number of quarters = 20
Step 3: Apply the present value formula:
The formula to calculate the present value of a future amount is:
Present Value = Future Value / (1 + Discount Rate)^Number of Periods
In this case, the future value is $7,000.00, the quarterly discount rate is 1.5%, and the number of periods is 20.
Substituting these values into the formula:
Present Value = $7,000.00 / (1 + 0.015)^20
Step 4: Calculate the present value:
Using a calculator or spreadsheet, calculate the present value based on the formula above:
Present Value = $7,000.00 / (1 + 0.015)^20
Present Value ≈ $5,231.22 (rounded to 2 decimal places)
Therefore, the present value of $7,000.00 in 5 years at a quarterly discount rate of 6% is approximately $5,231.22.