Applied Mathematics · Quick Reference

Financial Mathematics Cheat Sheet

Applied Mathematics · Lesson 6/7

In one line: 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.

Key Ideas

1Simple vs. Compound Interest. Simple interest grows linearly (same amount added each period); compound interest grows exponentially (interest earns interest on itself).

2Present 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.

3The 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.

4Annuities. A series of equal payments made at regular intervals, like monthly mortgage payments or retirement contributions.

5Risk and Return. Investments with higher potential returns generally come with higher risk (more variability in outcomes) -- a foundational tradeoff in finance.

Worked Examples

Find the future value of $1,000 invested at 5% annual compound interest for 3 years.

FV ≈ $1,157.63

Find the future value of the same $1,000 at 5% SIMPLE interest for 3 years.

FV = $1,150 (less than compound interest's $1,157.63)

Find the present value needed today to have $2,000 in 5 years at 4% annual compound interest.

PV ≈ $1,644

Formulas

Compound interest: FV = PV * (1 + r)^n

Simple interest: FV = PV * (1 + r*n)

Practice Yourself

Find FV of $500 at 6% compound interest for 2 years.

500*(1.06)^2 ≈ $561.80

Find FV of $500 at 6% simple interest for 2 years.

500*(1.12)=$560

What does 'present value' represent?

What a future sum of money is worth today