Interest Formulas

Overview

Engineering reference data for Interest Formulas in economics.

Key Formulas

Present Value

$PV = \frac{FV}{(1+r)^n}$

Discount a future value to present.

Net Present Value

$NPV = \sum_{t=0}^{n} \frac{C_t}{(1+r)^t}$

Sum of discounted cash flows.

Compound Interest

$FV = PV(1+r)^n$

Future value with compound interest.

Variables

Formulas and Examples

The core interest formulas involve discounting and accumulating cash flows.

Future Value (Single Cash Accumulation)

The accumulated value $F$ of a present sum $P$ invested at interest rate $i$ for $n$ periods is: $F = P(1 + i)^n$

• $P$: Principal or present sum (Future Value)
• $i$: Interest rate per period
• $n$: Number of interest periods

The factor $(1 + i)^n$ is the single payment compound amount factor.

Example: An amount of 1000 is invested at 10% annual interest for 10 years. $F = 1000 \times (1 + 0.1)^{10} = 2594$

Present Value (Discounting Process)

The present value $P$ of a future cash flow $F$ is calculated via discounting: $P = \frac{F}{(1 + i)^n}$

• $P$: Present value (Present Worth)
• $F$: Future cash flow
• $i$: Discount rate per period
• $n$: Number of periods

The factor $\frac{1}{(1 + i)^n}$ is the single payment present worth factor.

Example: A sum of 1000 is paid in 10 years. The discount rate is 10% per year. $P = \frac{1000}{(1 + 0.1)^{10}} = 386$

References

• Original Source