Mathematics of Finance for CA Foundation: Chapter Guide

What this chapter covers

Mathematics of Finance: topics in the order to study them

1. 1Simple Interest and Compound InterestEvery other topic depends on these two formulas, so you start here and fix the difference between linear and compounding growth.
2. 2Effective Rate of InterestIt extends compound interest to different compounding periods and teaches you to compare rates on one yearly basis.
3. 3Present Value, Future Value and Net Present ValueIt turns compound interest into discounting, which is needed for annuities, perpetuity and project evaluation.
4. 4Annuities: Ordinary, Due and Future ValueAn annuity is a series of equal payments, built by adding up present or future values, and it is the base for the next topics.
5. 5Perpetuity and Sinking FundPerpetuity is an annuity that never ends, and a sinking fund is an annuity used to reach a target sum, so both follow directly.
6. 6Capital Budgeting: IRR, Payback and Loan AmortizationThese need you to be comfortable with NPV and annuity present values, so they come after those topics.
7. 7Depreciation and Compound Annual Growth RateThese reuse the compound formula with a falling or measured growth rate, so they are quick once the earlier topics are clear.

How to prepare Mathematics of Finance

1. Write a one-page formula sheet in your own words as you finish each topic. Next to each formula, note when it applies, such as end-of-period or start-of-period payment.
2. Before using any formula, note three things: the rate per period, the number of periods, and whether payments fall at the start or end of each period. Convert the rate and periods to the same unit.
3. Practise powers and discount factors until they are quick. Learn small values such as (1.1)², (1.1)³, (1.05)² and (1.02)⁴ so you can spot the right option without a long calculation.
4. Solve questions by topic first, then mix them. In mixed sets, you should be able to name the pattern within ten seconds: single sum, annuity, perpetuity, project cash flows or depreciation.
5. Use option elimination. For a positive rate and a time of more than one compounding period (for example, t > 1 year with annual compounding), compound interest exceeds simple interest for the same sum at the same rate. A present value must be less than the future value at a positive rate. Remove options that break these checks.
6. Take timed MCQ sets of 20 questions. Mark any question that needs more than about two minutes, skip it, and return later. With four options and a 0.25 penalty, a blind guess is only about break-even (for a 1-mark question the expected gain is just a little above zero). Removing even one option makes guessing clearly favourable, so eliminate options first and then decide.
7. Keep an error log. Note whether each wrong answer was a formula error, a unit error or a calculation slip, and revise that category before each attempt.

Common mistakes in Mathematics of Finance

• Using the yearly rate with half-yearly or quarterly periods without converting.

  Fix: Divide the yearly rate by the number of periods per year and multiply the years by the same number. Do this as the very first step.

• Mixing up ordinary annuity and annuity due.

  Fix: Underline the words 'at the end' or 'at the beginning' in the question. For annuity due, multiply the ordinary annuity result by (1 + i).

• Reporting compound interest when the question asks for the amount, or the reverse.

  Fix: Check what is asked. Compound interest = amount − principal. Read the last line of the question before choosing.

• Treating NPV and IRR as the same thing.

  Fix: Remember that NPV gives a rupee value at a given rate, while IRR is the rate that makes NPV zero.

• Using straight line depreciation where the question says reducing balance, or forgetting scrap value.

  Fix: Identify the method first. For straight line, subtract scrap value from cost before dividing by the life.

• Making calculation slips with powers, and then choosing the closest option.

  Fix: Memorise common powers, calculate step by step, and use estimation to confirm the size of the answer before you mark it.

Last-day revision: Mathematics of Finance

• ✓Simple interest: SI = P × r × t, and amount A = P(1 + rt).
• ✓Compound interest: A = P(1 + r/n)^(nt), and CI = A − P.
• ✓Effective rate: E = (1 + r/n)ⁿ − 1, where r is the nominal yearly rate and n is compounding periods per year.
• ✓Future value of a single sum = PV × (1 + i)ⁿ, and present value = FV ÷ (1 + i)ⁿ.
• ✓NPV = present value of cash inflows − initial investment. Accept a project if NPV > 0.
• ✓Future value of an ordinary annuity = C × [(1 + i)ⁿ − 1] ÷ i, with payments at period end.
• ✓Annuity due = ordinary annuity × (1 + i), because each payment comes one period earlier.
• ✓Perpetuity present value = C ÷ i for an ordinary perpetuity. For a perpetuity due (first payment now), PV = C + C ÷ i, which is the same as (C ÷ i) × (1 + i).
• ✓Sinking fund payment = target amount × i ÷ [(1 + i)ⁿ − 1].
• ✓IRR is the rate at which NPV = 0. Payback period is the time taken to recover the initial investment.
• ✓Reducing balance depreciation: book value = cost × (1 − rate)ⁿ. Straight line: (cost − scrap) ÷ life per year.
• ✓CAGR = (ending value ÷ beginning value)^(1/n) − 1.

Mathematics of Finance practice questions

• A sum of money doubles itself in 10 years at simple interest. In how many years will it become four times itself at the same rate?
• Mr. Iyer wants a scheme that pays Rs 6,000 at the end of every year forever, with the first payment one year from today. If the rate of inte…
• Rajesh invests ₹50,000 in a fixed deposit that offers 8% per annum simple interest. How much interest will he earn after 3 years?
• A trust wants to give a scholarship of ₹15,000 at the end of every year forever, with the first payment one year from now. If money earns 7.…
• A project will pay Rs 10,000 at the end of each of years 3, 4 and 5 (three payments in all). Taking the discount rate as 10% p.a., the prese…
• The difference between compound interest (compounded annually) and simple interest on ₹20,000 for 2 years at 10% per annum is:
• Mehta Industries wants to accumulate ₹3,64,100 at the end of 3 years to replace equipment. It will make three equal deposits at the beginnin…
• A deposit earns interest at a nominal rate of 10% per annum, compounded half-yearly. What is the effective annual rate of interest?