Present Value and Future Value of a Single Amount: Core Concepts in Time Value of Money
- Graziano Stefanelli
- Apr 17
- 4 min read
In finance, every decision involves a trade-off between money now and money later.
This is the essence of the time value of money—the idea that a dollar today is worth more than a dollar tomorrow.
Before you dive into annuities, IRRs, or discounted cash flow models, you must understand how to move a single lump sum backward or forward in time.
This article walks through how to calculate both the present value and the future value of a single amount, and why these tools are foundational for financial modeling... and much more.
Understanding Time Value of Money
Money has a time dimension because of...
Opportunity cost: money today can be invested to earn a return
Inflation: money loses purchasing power over time
Risk: the future is uncertain, so future cash flows carry uncertainty
This is why receiving 1,000 today is not equal to 1,000 in one year.
To compare amounts across time, finance uses two core tools:
Compounding, to move money forward in time
Discounting, to bring money back to today
Example
If you had 1,000 today and could earn 5% annually, you'd have:
FV = 1,000 × 1.05 = 1,050 next year
So receiving 1,000 next year is worth less than 1,000 today—because you’re giving up the chance to earn interest.
The discount rate captures this opportunity cost.
Future Value of a Single Amount
The future value tells you how much an investment made today will grow to, based on compounding at a given rate.
It’s used when you know the present amount and want to calculate what it will become over time.
Formula
FV = P × (1 + r)^n
Where:
PÂ = present amount (initial investment)
r = interest rate per period
n = number of periods
Example: Investment Growth
You invest 5,000 today at an annual interest rate of 6% for 8 years.
P = 5,000
r = 0.06
n = 8
FV = 5,000 × (1.06)^8 = 5,000 × 1.593848 = 7,969.24
So after 8 years, your investment grows to 7,969.24.
Example 2: Quarterly Compounding
Now suppose you invest 5,000 at 6% annual interest, but it compounds quarterly for 8 years.
Annual rate = 6% → quarterly rate = 0.06 / 4 = 0.015
Periods = 8 × 4 = 32
FV = 5,000 × (1 + 0.015)^32 = 5,000 × 1.635 = 8,175.00
With more frequent compounding, your investment grows faster—even though the annual rate is the same.
Why It Matters
Compounding magnifies time and rate. The longer the period or the higher the rate, the larger the future value.
It also underlies key financial principles like compound interest, retirement projections, and long-term growth models.
Present Value of a Single Amount
The present value calculates what a future sum is worth today, using a discount rate.
It’s used when you expect to receive (or pay) a known amount in the future, and want to understand its current equivalent.
Formula
PV = F / (1 + r)^n
Where:
FÂ = future amount
r = interest rate per period
n = number of periods
Example: Discounting a Future Payment
You are promised 10,000 in 5 years, and your required return is 7% per year.
F = 10,000
r = 0.07
n = 5
PV = 10,000 / (1.07)^5 = 10,000 / 1.402552 = 7,128.55
This means that 10,000 received in 5 years is equivalent to 7,128.55 today, at a 7% rate.
Example 2: Business Decision
A supplier offers you two payment options:
Pay 9,000 today
Pay 10,000 in 1 year
If your cost of capital is 8%, the present value of the second option is:
PV = 10,000 / (1.08)^1 = 9,259.26
Since 9,259.26 > 9,000, the first option is cheaper in present value terms.
Why It Matters
PV calculations are essential for:
Comparing financial offers
Evaluating delayed payments
Pricing long-term contracts
They allow you to assess whether future cash flows meet your required return.
Use Cases in Business and Finance
These tools are used daily in financial decision-making...
Investment decisions: Should we invest now for a larger return later?
Loan analysis: How much is a future balloon payment worth today?
Valuation: What is the present value of a cash settlement, bond, or deferred revenue?
Insurance and pensions: What lump sum is equivalent to a future obligation?
For Financial Professionals
CFOs use PV to compare capital projects and budget cash flows.
Accountants apply discounting in lease accounting and impairment testing.
Analysts use FV to model retirement plans or future cost estimates.
Understanding PV/FV is the gateway to NPV, IRR, and DCFÂ models.
Using Excel for PV and FV
In Excel:
=FV(rate, nper, pmt, [pv], [type])
=PV(rate, nper, pmt, [fv], [type])
For single amounts:
FV =FV(0.06, 8, 0, -5000) → 7,969.24
PV =PV(0.07, 5, 0, -10000) → 7,128.55
Tips:
Use negative signs to reflect cash outflows (investments or payments).
Always match rate and period (monthly rate for monthly periods).
How Rate and Time Impact PV and FV
Small changes in rate or time have large effects.
The longer the period and the higher the rate, the more powerful compounding becomes.
Higher discount rates and longer time horizons shrink the present value.
___________
Being able to move a single amount forward or backward in time is the foundation of all financial analysis.
Use future value to understand how capital grows.
Use present value to make today’s decisions based on future outcomes.
Both are driven by the same inputs—rate and time—but they answer different questions:
What will this be worth? (FV)
What is this worth now? (PV)
Before modeling projects or pricing contracts, master these basic tools.
They’re the lens through which financial decisions are brought into focus.