PV of Lump Sum
Calculates the present value when discounting with periodic compounding.
When to use: Use when the discount rate compounds multiple times per year.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PV | Present Value | The current worth of a future sum | $ |
| FV | Future Value | The value of the investment at a future date | $ |
| 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: Trust Fund
A trust pays $200,000 in 12 years. Discount rate is 5% compounded semi-annually. What is today's value?
Given
Step-by-Step
The trust fund's present value is $110,582.44 with semi-annual discounting.
Example 2: Bond Maturity
A zero-coupon bond pays $1,000 at maturity in 5 years. Yield is 4% compounded quarterly.
Given
Step-by-Step
You should pay $819.54 for this bond to earn a 4% quarterly-compounded return.
Frequently Asked Questions
More frequent compounding results in a lower present value for the same nominal rate. This is because more frequent compounding makes money grow faster, so you need less today to reach the same future amount.
Use periodic discounting when the rate you are given compounds more often than annually — for example, a bond yield quoted with semi-annual compounding or a loan rate with monthly compounding. Matching the discounting frequency to the quoted rate ensures accuracy.
A zero-coupon bond is a bond that pays no interest during its life. Instead, it is sold at a discount and pays its full face value at maturity. The present value formula is used to determine what price to pay for the bond today.