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Revision GuideFinance & Business

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.

Filename: compound-interest-and-time-value-of-money-revision-guide.pdfFile size: 4 KB

Formula highlights

Compound growth
A = P(1 + r / n)^(nt)
Present value
PV = FV / (1 + r)^n

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.
Related calculators

Use the formulas in live tools.