Compound Interest and Time Value of Money Revision Guide
A deeper revision guide for simple interest, compound growth, present value, future value, and CAGR, with worked examples that show why time positioning changes the meaning of money.
Formula highlights
What this pack covers
Use this pack to keep the time value of money relationships visible when comparing growth, discounting, and the impact of compounding frequency.
Formula family
- A = P x (1 + r x t)
- A = P x (1 + r / n)^(n x t)
- PV = FV / growth factor
- FV = PV x growth factor
- CAGR = (ending / beginning)^(1 / years) - 1
Worked example: lump-sum compounding
1000 at 5 percent annually for 10 years grows to about 1628.89 under annual compounding. The result shows why time and reinvestment matter more than many first expect.
Worked example: present value thinking
A future amount only becomes comparable to a present decision once it is discounted back at a stated rate. Present value is the translation step that makes the comparison honest.
What CAGR does and does not tell you
CAGR gives a smoothed annual rate across the whole period. It is useful for comparison but says nothing about the volatility of the path taken to get there.
Common mistakes
- Comparing nominal rates with different compounding conventions as though they were identical.
- Using simple interest where returns are actually reinvested.
- Treating CAGR as a full risk story rather than a summary measure.
- Ignoring fees, inflation, or tax when interpreting the result in real life.
Use the formulas in live tools.
Compound Interest Calculator
Project compounded growth from a starting balance, contribution schedule, rate, and compounding frequency using only the values you enter.
Simple Interest Calculator
Use the Simple Interest Calculator to work out simple interest from values you control yourself, without baked-in policy assumptions.
Future Value Calculator
Calculate what a present amount grows to after the annual rate and time period you enter are applied.
Present Value Calculator
Discount a future amount back to today's terms using the annual rate and time period you enter.
CAGR Calculator
Use the CAGR Calculator to work out cagr from values you control yourself, without baked-in policy assumptions.