Lump Sum
A single amount moving through time. Given any three of present value, future value, rate and number of periods, solve for the fourth, under annual, periodic or continuous compounding.
FV of Lump Sum (Annual Compounding)
Calculates the future value of a single present amount invested at a fixed annual interest rate.
When to use: Use when you have a lump sum invested today and want to know its future worth with annual compounding.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| FV | Future Value | The value of the investment at a future date | $ |
| PV | Present Value | The current worth of a future sum | $ |
| k | Interest Rate | Nominal annual interest rate as a decimal | % |
| n | Number of Years | Investment time horizon in years | years |
Real-Life Examples
Example 1: Retirement Investment
Sarah invests $10,000 in a mutual fund earning 7% annually. How much will she have in 20 years?
Given
Step-by-Step
For these inputs, Future Value is $38,696.84 under the stated payment, compounding and accounting assumptions.
Example 2: College Savings
Mark puts $5,000 into a savings bond earning 5% annually for his newborn. What is it worth in 18 years?
Given
Step-by-Step
For these inputs, Future Value is $12,033.10 under the stated payment, compounding and accounting assumptions.
Frequently Asked Questions
The future value of a lump sum is the amount a single investment made today will grow to over a specified period at a given interest rate. It accounts for the effect of compound interest over time.
Compound interest earns interest on previously earned interest, causing your investment to grow exponentially rather than linearly. The longer the time period, the more dramatic the compounding effect becomes.
Future value tells you what a current amount will be worth later, while present value tells you what a future amount is worth today. They are inverse calculations — if you know one, you can find the other.
The Rule of 72 is a quick way to estimate how long it takes to double your money. Divide 72 by the annual interest rate (as a whole number) to get the approximate doubling time in years. For example, at 8% it takes roughly 72 ÷ 8 = 9 years to double.