Cumulative Discount Factor

Cumulative Discount Factor Formula:

\[ \text{CDF} = \sum_{t=1}^{n} \frac{1}{(1 + r)^t} \]

Cumulative Discount Factor:

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1. What is Cumulative Discount Factor?

The Cumulative Discount Factor (CDF) is the sum of discount factors for multiple periods. It's used in finance to calculate the present value of a series of future cash flows.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{CDF} = \sum_{t=1}^{n} \frac{1}{(1 + r)^t} \]

Where:

$ r $ — Discount rate per period (decimal)
$ n $ — Number of periods
$ t $ — Current period (from 1 to n)

Explanation: The formula sums the present value factors for each period from 1 to n.

3. Importance of Cumulative Discount Factor

Details: CDF is essential for calculating the present value of annuities, lease payments, and other regular cash flow streams in financial analysis and capital budgeting.

4. Using the Calculator

Tips: Enter the discount rate as a decimal (e.g., 0.05 for 5%) and the number of periods. Both values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between discount factor and cumulative discount factor?
A: Discount factor is for a single period, while CDF sums discount factors for multiple periods.

Q2: How is this related to annuity calculations?
A: The CDF is essentially the present value factor for an ordinary annuity of $1 per period.

Q3: Can I use this for monthly cash flows?
A: Yes, but ensure the discount rate matches the period (use monthly rate for monthly periods).

Q4: What if my discount rate changes over time?
A: This calculator assumes a constant rate. For varying rates, you'd need to calculate each period separately.

Q5: How does this relate to NPV calculations?
A: NPV uses discount factors for each period's cash flow, while CDF sums the discount factors themselves.