Present Value: Less Than 1 Year
Sometimes cash arrives in 3, 6 or 9 months, not in whole years. To find its present value, express the time as a fraction of a year and use that fraction as the exponent when you discount at the annual rate.
What you will learn
- How to turn months into a fraction of a year for discounting
- The present value formula with a fractional exponent
- How the compound and simple interest answers compare
- How to avoid mixing annual and monthly rates
The formulas
- FV
- amount to be received
- r
- annual discount rate
- m
- number of months until payment
- r
- annual rate
- m
- number of months
Worked example
You will receive $1,000 in 9 months. The annual discount rate is 8%, compounded annually. What is it worth today?
- Convert the time: 9 months = 9 ÷ 12 = 0.75 years.
- Discount factor base: (1.08)^0.75 ≈ 1.05942.
- Divide: PV = $1,000 ÷ 1.05942 ≈ $943.91.
- For comparison, simple interest gives $1,000 ÷ (1 + 0.08 × 0.75) ≈ $943.40.
Answer: About $943.91 today with compound discounting (rounded to the cent).
Common questions
How do you calculate present value for less than one year?
Express the time as a fraction of a year and use it as the exponent: PV = FV ÷ (1 + r)^(months ÷ 12). For $1,000 due in 9 months at 8%, PV = $1,000 ÷ 1.08^0.75 ≈ $943.91.
Can I use a decimal number of years in the present value formula?
Yes. The exponent can be any number, including 0.25 or 0.75. It means you are discounting for part of a year at the annual rate. Use the power key on your calculator.
Is the present value for 6 months just half a year of interest?
Not exactly, under compound interest. At 8% a year, half a year of compounding is 1.08^0.5 ≈ 1.0392, not 1.04. The 1.04 figure is the simple interest version, which some short-term problems use.
What if the rate is compounded monthly instead?
Then use the monthly rate and count months: PV = FV ÷ (1 + r ÷ 12)^m. The fractional exponent method is for a rate quoted as compounded annually.