Sunflower Intelligence
Finance & Accounting

F04 · Introductory

Mathematics of Finance

9 lessons

F04 · Introductory · 9 lessons in four modules · about 12.5 hours

Mathematics of Finance

Interest, present and future value, annuities, loans and inflation, with every formula worked step by step.

What you will learn

  • Calculate simple and compound interest, and solve compound-growth problems for the amount, the rate or the time.
  • Convert between nominal, periodic and effective annual rates for any compounding frequency, including continuous compounding, and use them to compare offers.
  • Calculate the present and future value of single amounts and of uneven cash-flow streams, the net present value of a decision, and the internal rate of return by trial.
  • Value annuities, annuities due, growing annuities and perpetuities, and solve for the payment, the number of periods or the rate.
  • Build a loan amortisation schedule, find the balance outstanding at any date, and compare loans, instalment plans and refinancing.
  • Distinguish nominal from real amounts and rates, discount consistently, and analyse a fixed-rate mortgage including points and term, and how an adjustable rate resets.

Prerequisites

How it works

Each lesson teaches the idea from first principles, works examples step by step, lets you explore it in an interactive, then has you practise with feedback. A lesson is complete when you have worked its guided problems and scored 80% on its knowledge check. Mastery is tracked separately and comes back for review before you are likely to forget. Each module ends with a test; the course ends with a project and a final assessment.

Fictional case

Lantern Coffee Co. A fictional coffee business founded by Ana Lim. It starts as a catering and barista-training service, opens its own cafés and an online shop for beans, and plans a canned cold brew. Every name and figure in it is invented for teaching.

Not sure where to start?

The diagnostic has 12 questions across the course. It doesn’t count toward anything; it suggests the module to start from. Take the diagnostic.

Modules and lessons

Module 1 Interest

  1. Simple and compound interestInterest is charged in one of two ways: on the principal only, or on the principal and the interest already earned. Learn to calculate both for any length of time, to count days the way loan contracts do, and to work backwards from two amounts to the rate or the time that links them.80 min · not started
  2. Effective annual ratesA rate of 7.2% a year can cost 7.2%, 7.40% or 7.47% a year depending on how often interest is compounded. Learn to tell nominal, periodic and effective rates apart, to convert any rate to any compounding frequency (continuous compounding included), to read a US annual percentage yield, and to compare offers quoted in different ways.75 min · not started
  3. Module 1 test12 questions on this module. 70% passes.not taken

Module 2 Present and future value

  1. Present and future valueAn amount of money has a different value at every date. Learn to draw a timeline, discount single amounts with discount factors, move any amount to any date, cope with rates that change, and solve for the missing amount, rate or time, so that amounts at different dates can be compared fairly.90 min · not started
  2. Discounting cash flowsMost real streams of money are uneven: a loan pays interest and then its principal, a project costs money now and returns different amounts later. Learn to value any stream by discounting each cash flow, to judge a decision by its net present value, and to find the rate of return that makes that value zero.90 min · not started
  3. Module 2 test11 questions on this module. 70% passes.not taken

Module 3 Streams of cash

  1. AnnuitiesLoan instalments, rent, leases, pensions and savings plans are all streams of equal payments. Learn to value such a stream in one step, whether the payments come at the end or the start of each period, start now or later, stay level or grow, and to solve for the payment, the number of payments or the rate.80 min · not started
  2. Perpetuities and growthA payment that never stops still has a finite value today. Learn to value level and growing perpetuities, including ones that start now or later, price a preferred share, size an endowment, and see why anything valued as growing forever depends so heavily on the gap between the discount rate and the growth rate.75 min · not started
  3. Loan amortisationAn instalment loan is an annuity seen from the borrower’s side. Learn to calculate the payment, build a schedule that splits each payment into interest and principal, find the balance owed at any date, and use those tools to compare loans and instalment plans, to judge prepaying or refinancing, and to see what fees do to the APR.90 min · not started
  4. Module 3 test11 questions on this module. 70% passes.not taken

Module 4 Real versus nominal

  1. Inflation and real returnsA dollar next year is not the same unit as a dollar today. Measure inflation over several years, convert amounts into today’s dollars, use the exact Fisher relation, and discount nominal cash flows at nominal rates and real cash flows at real rates, so that every comparison across time is made in one kind of dollar.85 min · not started
  2. MortgagesA home loan is an annuity with a house attached. Calculate a fixed-rate mortgage payment, compare 30- and 15-year terms, find the balance after any number of years, decide whether discount points and extra payments pay off, see what inflation does to a fixed payment, and read how an adjustable-rate mortgage resets.85 min · not started
  3. Module 4 test12 questions on this module. 70% passes.not taken

Project and final assessment

  1. Project: Ana’s home planPlan how Ana saves a home deposit and which mortgage she takes: a savings schedule, two mortgage offers, points, the balance after five years and what the payments are worth after inflation.not taken
  2. Final assessment24 questions across the whole course. 70% passes.not taken

The course is complete when every lesson is complete, every module test is passed, the project is finished and the final assessment is passed.

Resources

  • Glossary: every term this course defines.
  • Formulas: every formula with its symbols and units.
  • Review: flashcards and the questions you missed, when they are due.

Elsewhere on this site

Sources used in this course

  1. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 7.2, “Time Value of Money (TVM) Basics”. OpenStax. openstax.org/books/principles-finance/pages/7-2-time-value-o…
  2. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 7.3, “Methods for Solving Time Value of Money Problems” (solving for the number of periods and the rate). OpenStax. openstax.org/books/principles-finance/pages/7-3-methods-for-…
  3. Kirk, D. (2023). Contemporary Mathematics, section 6.3, “Simple Interest”. OpenStax. openstax.org/books/contemporary-mathematics/pages/6-3-simple…
  4. Abramson, J. (2021). College Algebra 2e, section 6.6, “Exponential and Logarithmic Equations”. OpenStax. openstax.org/books/college-algebra-2e/pages/6-6-exponential-…
  5. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 8.4, “Stated versus Effective Rates”. OpenStax. openstax.org/books/principles-finance/pages/8-4-stated-versu…
  6. Kirk, D. (2023). Contemporary Mathematics, section 6.4, “Compound Interest” (compounding frequency and effective annual yield). OpenStax. openstax.org/books/contemporary-mathematics/pages/6-4-compou…
  7. Consumer Financial Protection Bureau. Regulation DD (Truth in Savings), 12 CFR part 1030, Appendix A: Annual Percentage Yield Calculation. consumerfinance.gov/rules-policy/regulations/1030/a
  8. Federal Deposit Insurance Corporation. Consumer Compliance Examination Manual, chapter VI-3, “Truth in Savings” (Regulation DD). Last updated May 2023. fdic.gov/consumer-compliance-examination-manual/vi-3-truth-s…
  9. National Credit Union Administration. Truth in Savings Act (NCUA Rules and Regulations Part 707), Federal Consumer Financial Protection Guide. ncua.gov/regulation-supervision/manuals-guides/federal-consu…
  10. Consumer Financial Protection Bureau. Regulation Z (Truth in Lending), 12 CFR §1026.3: Exempt transactions. consumerfinance.gov/rules-policy/regulations/1026/3
  11. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 7.4, “Applications of TVM in Finance”. OpenStax. openstax.org/books/principles-finance/pages/7-4-applications…
  12. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 9.1, “Timing of Cash Flows” (uneven or mixed streams). OpenStax. openstax.org/books/principles-finance/pages/9-1-timing-of-ca…
  13. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 16.2, “Net Present Value (NPV) Method”. OpenStax. openstax.org/books/principles-finance/pages/16-2-net-present…
  14. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 16.3, “Internal Rate of Return (IRR) Method”. OpenStax. openstax.org/books/principles-finance/pages/16-3-internal-ra…
  15. Microsoft. NPV function (Excel help: timing of the values, and adding a first-period cash flow outside the function). support.microsoft.com/office/npv-function-8672cb67-2576-4d07…
  16. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 8.2, “Annuities”. OpenStax. openstax.org/books/principles-finance/pages/8-2-annuities
  17. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 8.5, “Equal Payments with a Financial Calculator and Excel”. OpenStax. openstax.org/books/principles-finance/pages/8-5-equal-paymen…
  18. Microsoft Support. RATE function (Excel). support.microsoft.com/en-us/office/rate-function-9f665657-4a…
  19. US Securities and Exchange Commission, Investor.gov. Annuities. investor.gov/introduction-investing/investing-basics/investm…
  20. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 8.1, “Perpetuities”. OpenStax. openstax.org/books/principles-finance/pages/8-1-perpetuities
  21. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 11.2, “Dividend Discount Models (DDMs)”. OpenStax. openstax.org/books/principles-finance/pages/11-2-dividend-di…
  22. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 11.4, “Preferred Stock”. OpenStax. openstax.org/books/principles-finance/pages/11-4-preferred-s…
  23. US Securities and Exchange Commission, Investor.gov. Stocks – FAQs (common and preferred stock). investor.gov/introduction-investing/investing-basics/investm…
  24. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 8.3, “Loan Amortization”. OpenStax. openstax.org/books/principles-finance/pages/8-3-loan-amortiz…
  25. Consumer Financial Protection Bureau. Regulation Z, Appendix J to Part 1026: Annual Percentage Rate Computations for Closed-End Credit Transactions. consumerfinance.gov/rules-policy/regulations/1026/j
  26. Consumer Financial Protection Bureau. Regulation Z, 12 CFR §1026.4: Finance charge. consumerfinance.gov/rules-policy/regulations/1026/4
  27. Consumer Financial Protection Bureau. Regulation Z, 12 CFR §1026.3: Exempt transactions. consumerfinance.gov/rules-policy/regulations/1026/3
  28. Consumer Financial Protection Bureau. What is a prepayment penalty? consumerfinance.gov/ask-cfpb/what-is-a-prepayment-penalty-en…
  29. US Bureau of Labor Statistics. Consumer Price Index (programme home page). bls.gov/cpi
  30. US Bureau of Labor Statistics. How to Use the Consumer Price Index for Escalation. Fact sheet, last modified 8 June 2023. bls.gov/cpi/factsheets/escalation.htm
  31. US Department of the Treasury, Bureau of the Fiscal Service. Treasury Inflation-Protected Securities (TIPS). TreasuryDirect. treasurydirect.gov/marketable-securities/tips
  32. US Department of the Treasury, Bureau of the Fiscal Service. TIPS/CPI Data: reference CPI numbers and daily index ratios. TreasuryDirect. treasurydirect.gov/instit/annceresult/tipscpi/tipscpi.htm
  33. Dahlquist, J. & Knight, R. (2022). Principles of Finance, section 3.4, “Interest Rates”. OpenStax. openstax.org/books/principles-finance/pages/3-4-interest-rat…
  34. Consumer Financial Protection Bureau. What are (discount) points and lender credits and how do they work? consumerfinance.gov/ask-cfpb/what-are-discount-points-and-le…
  35. Consumer Financial Protection Bureau. What is the difference between a mortgage interest rate and an APR? Last reviewed 28 August 2026. consumerfinance.gov/ask-cfpb/what-is-the-difference-between-…
  36. Consumer Financial Protection Bureau. What is an escrow or impound account? consumerfinance.gov/ask-cfpb/what-is-an-escrow-or-impound-ac…
  37. Consumer Financial Protection Bureau. For an adjustable-rate mortgage (ARM), what are the index and margin, and how do they work? consumerfinance.gov/ask-cfpb/for-an-adjustable-rate-mortgage…
  38. Consumer Financial Protection Bureau. With an adjustable-rate mortgage (ARM), what are rate caps and how do they work? Last reviewed 14 January 2025. consumerfinance.gov/ask-cfpb/with-an-adjustable-rate-mortgag…