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📘 Lesson 6 of 7 · Applied Mathematics

💰 Financial Mathematics

Financial mathematics applies mathematical tools to money — interest, investments, loans, and risk — giving precise answers to questions about how wealth grows or shrinks over time.

Course progress: 86%

01 Key Concepts

Simple vs. Compound Interest

Simple interest grows linearly (same amount added each period); compound interest grows exponentially (interest earns interest on itself).

Present Value and Future Value

Future value (FV) is what money grows to over time; present value (PV) is what a future amount is worth today, accounting for the time value of money.

The Time Value of Money

A dollar today is worth more than a dollar in the future, because today's dollar can be invested and earn interest in the meantime.

Annuities

A series of equal payments made at regular intervals, like monthly mortgage payments or retirement contributions.

Risk and Return

Investments with higher potential returns generally come with higher risk (more variability in outcomes) -- a foundational tradeoff in finance.

02 Key Formulas

03 Solved Examples

Example 1 Find the future value of $1,000 invested at 5% annual compound interest for 3 years.
  1. Apply the formula: FV = PV*(1+r)^n = 1000*(1.05)^3.
  2. (1.05)^3 ≈ 1.157625.
  3. 1000 * 1.157625.
Answer: FV ≈ $1,157.63
Example 2 Find the future value of the same $1,000 at 5% SIMPLE interest for 3 years.
  1. Apply the formula: FV = PV*(1+r*n) = 1000*(1+0.05*3).
  2. = 1000*(1.15).
Answer: FV = $1,150 (less than compound interest's $1,157.63)
Example 3 Find the present value needed today to have $2,000 in 5 years at 4% annual compound interest.
  1. Rearrange FV=PV*(1+r)^n to solve for PV: PV = FV/(1+r)^n.
  2. PV = 2000/(1.04)^5.
  3. (1.04)^5 ≈ 1.2167.
  4. PV = 2000/1.2167.
Answer: PV ≈ $1,644

04 Practice Questions

1Find FV of $500 at 6% compound interest for 2 years.
500*(1.06)^2 ≈ $561.80
2Find FV of $500 at 6% simple interest for 2 years.
500*(1.12)=$560
3What does 'present value' represent?
What a future sum of money is worth today
4Why is a dollar today worth more than a dollar next year?
Because it can be invested and earn interest in the meantime (time value of money)
5What is an 'annuity'?
A series of equal payments made at regular intervals

📄 Financial Mathematics — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet