The Time Game: A Journey Through Interest, Compounding & Discounting
“Discounting allows us to compare different streams of cash flows fairly, recognising that a dollar received today is worth more than a dollar received in the future, due to time, risk, and inflation.”
Imagine two friends — Sara and Omar — both received £1,000 on their 21st birthday. Instead of spending it, they decided to invest. What followed wasn't just a story of money — but a lesson in how time and interest shape value.
This is where our journey begins — with the concept of interest.
Understanding Interest – The Reward for Time
Interest is the cost of borrowing money — or the reward for lending it. When you lend or invest money, interest is what you earn. When you borrow, it’s what you pay. It's the price tag of time.
Omar, ever the minimalist, put his £1,000 in a traditional deposit account that offered simple interest — predictable, consistent, and… well, a little plain.
Sara, on the other hand, explored something a bit more powerful: compound interest.
Let’s see how their stories unfolded.
Simple Interest – The Straight Path
Omar’s bank promised him 5% simple interest per year. That meant every year, he’d earn £50, no matter how long the money stayed there.
So after 3 years, Omar would have £150 (£50 pa x 3 years) in interest and the total value of the investment would be £1,150. (£1,000 + £150)
You can find the value of your investment by using the following formula:
Future Value = Principal + (Number of years x Interest Rate x Principal)
Simple. Predictable. But not particularly exciting.
Compound Interest – The Growth Mindset
Sara chose an account offering 5% compound interest — where interest is reinvested and earned on interest. The magic of compounding had begun.
After 3 years, her calculation looked like this:
£1,000 x 1.05 = £1,050
£1,050 x 1.05 = £1,102.50
£1,102.50 x 1.05 = £1,157.63
So Sara had £1,157.63, while Omar had £1,150.
You can find the value of your investment using the following formula
Future Value = Principal x (1 + Interest Rate)^number of years
The difference? Small now. But fast forward 10, 15, 20 years — and Sara’s money would snowball into something much larger. That’s the power of compounding — it rewards time and patience exponentially.
Let’s pause here and define compounding more clearly.
Compounding is the process where:
Interest earns interest.
Each period, interest is added to the principal, forming a new base for the next round of interest.
It’s what happens when you reinvest your earnings instead of withdrawing them. The more frequent the compounding (monthly, quarterly, annually), the faster your money grows.
In short:
Simple interest = interest on the principal
Compound interest = interest on principal + past interest
Discounting – Reversing the Clock
Now imagine Sara wants to know the todays /present value of $1,157.63 she expects to receive three years from now.
This is where discounting enters — the reverse of compounding.
It answers the question:
"What is the value today of a future amount of money?"
Using the same 5% rate, the formula flips:
Present Value/Principal Amount = Future Value / (1 + Interest Rate)^No of years
= $1,157.63 / (1.05)^3 ≈ $1,000
Just like that, she’s back to her starting point.
Discounting is what businesses use to assess investment projects, and what financial analysts use to value future cash flows. It's how discounted cash flow techniques like Net Present Value (NPV), Internal Rate of Return (IRR), and Discounted Payback Period bring future money into today’s terms.
By applying a discount rate—often reflecting the cost of capital, risk, or opportunity cost—these methods help decision-makers determine whether a project is financially viable. If the present value of expected inflows exceeds the initial investment, the project adds value. Otherwise, it may be rejected.
Ultimately, discounting allows us to compare different streams of cash flows fairly, recognising that a dollar received today is worth more than a dollar received in the future, due to time, risk, and inflation.
