FV of Lump Sum
Calculates the future value when interest compounds multiple times per year.
When to use: Use when interest compounds monthly, quarterly, or at other periodic intervals.
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 |
| m | Compounding Frequency | Number of times interest compounds per year | integer |
Real-Life Examples
Example 1: Monthly Compounding CD
You deposit $25,000 in a CD earning 4.5% compounded monthly for 5 years.
Given
Step-by-Step
The CD will be worth $31,304.95 after 5 years with monthly compounding.
Example 2: Quarterly Compounding Savings
An inheritance of $50,000 is placed in an account earning 6% compounded quarterly for 10 years.
Given
Step-by-Step
The inheritance grows to $90,700.41 with quarterly compounding over 10 years.
Frequently Asked Questions
Compounding frequency is how often earned interest is added to the principal balance. Common frequencies include monthly (12 times/year), quarterly (4 times/year), semi-annually (2 times/year), and daily (365 times/year).
Yes, more frequent compounding always produces a higher future value for the same nominal interest rate. However, the incremental benefit decreases as compounding frequency increases — the jump from annual to monthly is larger than from monthly to daily.
Divide the annual nominal rate by 12 to get the monthly periodic rate. For example, a 6% annual rate becomes 0.5% per month (0.06 ÷ 12 = 0.005). This periodic rate is used in the compounding formula.
APR (Annual Percentage Rate) is the stated annual rate before accounting for compounding. The periodic rate is the APR divided by the number of compounding periods per year. For example, a 12% APR compounded monthly has a periodic rate of 1% per month.