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Present Value of Annuity with Continuous Compounding Formula:
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The Present Value of Annuity with Continuous Compounding calculates the current worth of a series of future cash flows where interest is compounded continuously. It accounts for the time value of money under continuous compounding conditions.
The calculator uses the formula:
Where:
Explanation: The formula discounts each future cash flow back to the present value using continuous compounding, then sums these present values to get the total annuity value.
Details: Calculating present value is essential for investment analysis, retirement planning, loan amortization, and any financial decision involving future cash flows. Continuous compounding provides the most accurate compounding model.
Tips: Enter cashflow per period in dollars, rate per period as a decimal (e.g., 0.05 for 5%), and number of periods. All values must be positive.
Q1: What is continuous compounding?
A: Continuous compounding assumes that interest is compounded an infinite number of times per period, providing the theoretical maximum compounding effect.
Q2: How does continuous compounding differ from discrete compounding?
A: Continuous compounding uses the mathematical constant e, while discrete compounding uses (1 + r/n)^(n*t). Continuous compounding generally yields slightly higher values.
Q3: When is continuous compounding used in practice?
A: While rarely used in consumer banking, continuous compounding is common in mathematical finance, option pricing models, and theoretical economic analysis.
Q4: What is Napier's constant (e)?
A: e is a mathematical constant approximately equal to 2.71828, which is the base of the natural logarithm and fundamental to continuous growth processes.
Q5: Can this formula be used for both ordinary and annuity due?
A: This formula calculates the present value of an ordinary annuity (payments at period end). For annuity due (payments at period beginning), multiply the result by e^r.