Discrete Compounding Cash Flow Formulas

Single Payment

Compound Amount

Converts a single payment (or value) today to a future value.

Formula: F = P(1 + i)^n

Where:

• F = future value
• P = single payment today
• i = interest rate per period
• n = number of periods

Present Worth (or Value)

Converts a future payment (or value) to present worth (or value).

Formula: P = F(1 + i)^-n

Where:

• P = present value
• F = single future payment
• i = discount rate per period
• n = number of periods

Uniform Series

Compound Amount - Annuity

Converts a uniform amount (annuity) to a future value.

Formula: F = A × ((1 + i)^n - 1) / i

Where:

• F = future value
• A = uniform amount per period
• i = interest rate
• n = number of periods

Sinking Fund

Converts a specific future value to uniform amounts (annuities).

Formula: A = F × i / ((1 + i)^n - 1)

Where:

• A = uniform amount per period
• F = future value
• i = interest rate
• n = number of periods

Present Worth - Uniform Series

Converts a uniform amount (annuity) to a present value.

Formula: P = A × ((1 + i)^n - 1) / (i × (1 + i)^n)

Where:

• P = present value
• A = amount per interest period
• i = discount rate
• n = discount periods

Capital Recovery

Converts a present value to a uniform amount (annuity).

Formula: A = P × (i × (1 + i)^n) / ((1 + i)^n - 1)

Where:

• P = present value
• A = amount per interest period
• i = interest rate
• n = discount periods