Discrete Payments Compounding Formulas

Reference data and engineering information about discrete payments compounding formulas for basics applications.

discretepaymentscompoundingformulas

Overview

Engineering reference data for Discrete Payments Compounding Formulas in basics.

Key Formulas

Conservation of Energy

$E_{in} = E_{out} + \Delta E_{stored}$

Energy balance.

Variables

Symbol	Description	Unit
$V$	Voltage	V
$I$	Current	A
$R$	Resistance	Ω
$F$	Force	N
$m$	Mass	kg
$a$	Acceleration	m/s²

For engineers implementing these formulas in code or spreadsheets, the standard implementations often use the base formula with variables as defined. Here's a consolidated reference table of the primary formulas and their common computational names:

6 rows

Summary of core discrete compounding formulas and their primary application context.
Formula Name	Common Variable	Solve For	Typical Use Case
Single Payment Compound Amount	F = P(1+i)^n	Future Value (F)	Growing a lump sum investment.
Present Worth (Single)	P = F(1+i)^-n	Present Value (P)	Discounting a single future cash flow.
Uniform Series Compound Amount	F = A[ (1+i)^n - 1 ] / i	Future Value (F)	Future value of periodic savings or payments.
Sinking Fund	A = F[ i / ( (1+i)^n - 1 ) ]	Annuity (A)	Required periodic deposit to reach a target future sum.
Present Worth (Annuity)	P = A[ ( (1+i)^n - 1 ) / ( i(1+i)^n ) ]	Present Value (P)	Present value of a series of future payments.
Capital Recovery	A = P[ i(1+i)^n / ( (1+i)^n - 1 ) ]	Annuity (A)	Periodic payment needed to repay a present loan amount with interest.

Source: engineeringtoolbox.com

Practical Application Notes

When applying these formulas, ensure the interest rate i is expressed as a decimal per period (e.g., 5% -> 0.05). The period n must match the compounding frequency of i. For example, if using a monthly interest rate, n must be the number of months.

These relationships are fundamental for financial modeling in engineering projects, including capital budgeting, loan amortization, sinking fund planning, and evaluating the time value of money for equipment investments or project cash flows.

References

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