CMA Foundation · Fundamentals of Business Mathematics and Statistics
Time Value of Money and Annuity: Simple and Compound Interest
Time value of money means ₹1 today is worth more than ₹1 later because it can earn interest. You solve problems by picking the right formula: simple interest for flat growth, compound interest for interest on interest, and annuity formulas for equal payments at regular intervals. Match the rate to the period first.
What this chapter covers
This chapter shows how money grows or shrinks over time. It starts with simple interest, where interest is earned only on the original principal. It then moves to compound interest, where interest is added to the principal and earns interest itself. You also learn how the compounding period (yearly, half-yearly, quarterly, monthly) changes the answer.
The second half deals with present value, future value, depreciation and annuities. Present value tells you what a future sum is worth today. Future value tells you what money today becomes later. An annuity is a series of equal payments at equal intervals, such as an EMI or a recurring deposit.
The chapter links to the rest of Paper 3 through ratios, percentages, powers and logarithm-style calculations. It also helps in Paper 2 (depreciation) and Paper 4 (basic ideas of investment and cost of capital). Most questions are short numerical MCQs, so speed with clean formulas matters.
This chapter gives you formula-driven questions where one correct method leads straight to one answer, so it is a reliable place to collect marks in a 50-question, one-hour paper with no negative marking. The numbers in exam questions are usually simple, and the same few formulas repeat in different forms. Once you fix the formulas and the rate-period matching habit, you can aim to solve most questions in about a minute each and save time for harder chapters.
Time Value of Money and Annuity - Simple and Compound Interest: topics in the order to study them
- 1Simple InterestIt is the base idea: interest on principal only. Everything later builds on I = P × r × t.
- 2Compound Interest and Compounding PeriodsNext you add interest on interest and learn to adjust rate and number of periods for half-yearly, quarterly or monthly compounding.
- 3Nominal and Effective Rate of InterestThis needs compounding periods first, because the effective rate is the yearly rate that gives the same result as the nominal rate compounded more often.
- 4Present Value, Future Value and DepreciationThese reuse the compound formula, rearranged to find the starting amount or the reducing value of an asset.
- 5Annuity: Immediate, Due and PerpetuityAnnuities are the hardest part, since they sum a series of equal payments. Study them last, once PV and FV are comfortable.
How to prepare Time Value of Money and Annuity - Simple and Compound Interest
Aim to learn few formulas deeply and practise them in varied wording. Work with a pen and paper, even if you study on your phone.
- Write the formulas on one page: SI = P × r × t ÷ 100, A = P(1 + r/100)^n, CI = A − P, and effective rate = (1 + i/m)^m − 1.
- For every question, first match the rate and the time period. If compounding is quarterly, divide the annual rate by 4 and multiply the years by 4.
- Practise simple interest and compound interest with round numbers such as ₹10,000 at 10% until you can do two-year and three-year cases mentally.
- Learn the difference between present value and future value by drawing a small timeline for each question: where is the money now, and where will it be.
- For annuities, decide first whether payments come at the end of each period (immediate or ordinary) or at the start (due), then apply the correct formula. Treat perpetuity as payment ÷ rate.
- Do timed sets of 10 MCQs in 10 minutes. After each set, note which formula you forgot or which unit you mismatched.
- In the last week, redo only your error notes and the one-page formula sheet.
Common mistakes in Time Value of Money and Annuity - Simple and Compound Interest
Using the annual rate with the number of quarters or months
Fix: Write rate per period and number of periods on the first line of every solution before calculating.
Giving the amount when the question asks for compound interest
Fix: Underline what is asked. Subtract the principal when the question asks for interest.
Confusing nominal and effective rate
Fix: Remember that the nominal rate is the quoted rate, and the effective rate is the true yearly rate after compounding.
Mixing up annuity immediate and annuity due
Fix: Check the payment timing. If it is at the start of each period, multiply the immediate-annuity value by (1 + r).
Using percentage values directly in formulas that need decimals
Fix: Convert 8% to 0.08 whenever the formula has no ÷ 100. Use one form consistently.
Applying simple interest logic to depreciation or growth questions
Fix: Read the method word carefully: straight-line uses a fixed amount each year; reducing balance uses a percentage of the current value.
Last-day revision: Time Value of Money and Annuity - Simple and Compound Interest
- Simple interest: SI = P × r × t ÷ 100; amount = P + SI.
- Compound amount: A = P(1 + r/100)^n; CI = A − P.
- For compounding m times a year, use rate ÷ m per period and n × m periods.
- At the same rate, CI is greater than SI for periods longer than one compounding period. For one compounding period (e.g. one year with yearly compounding), CI = SI.
- Effective rate = (1 + i/m)^m − 1, where i is the nominal annual rate as a decimal.
- More frequent compounding gives a higher effective rate than the nominal rate.
- Present value = Future value ÷ (1 + r)^n.
- Reducing balance depreciation: value = cost × (1 − d)^n.
- Immediate annuity payments are made at the end of each period; annuity due at the start.
- Annuity due value = immediate annuity value × (1 + r).
- Perpetuity present value = payment ÷ rate, with the rate as a decimal.
- Always check whether the question asks for amount, interest, or rate.
Time Value of Money and Annuity - Simple and Compound Interest practice questions
- In how many years will a sum of money double itself at 10% per annum compound interest if the amount after 7 years is 1.95 times the sum and…
- A sum of money lent at simple interest amounts to Rs 13,600 in 3 years and to Rs 15,200 in 5 years. What is the rate of simple interest per …
- Mr. Sharma invests Rs 20,000 for 2 years at 10% per annum, compounded annually. What is the compound interest earned at the end of 2 years?
- Ms. Kavita deposits Rs 5,000 at the end of each year for 3 years in an account earning 10% p.a. compound interest. What will be the accumula…
- Mr. Iyer buys a security that pays Rs 6,000 at the end of every year forever. If the required rate of return is 8% per annum, what is the pr…
- Rs 10,000 is invested at a nominal rate of 20% per annum compounded quarterly. What will be the amount at the end of 6 months? (Use simple a…
- A person invests Rs 5,000 at the end of each year for 2 years at 20% p.a. compound interest. What is the amount at the end of year 2?
- Mr. Sharma lends Rs 25,000 to a friend at 8% per annum simple interest. How much interest will he earn in 3 years?
Time Value of Money and Annuity - Simple and Compound Interest in other exams
The same ground in other exams, if you are preparing for more than one or want another angle on it.
Time Value of Money and Annuity - Simple and Compound Interest: frequently asked questions
Do I need to memorise many formulas for this chapter?
Only a small set: simple interest, compound amount, effective rate, present value, and the annuity and perpetuity formulas. Most questions are variations of these. Learn them with one worked example each.
Will I get a calculator in the CMA Foundation exam?
Do not rely on one. Practise with simple numbers and use mental arithmetic and elimination. Check the latest ICMAI exam instructions for the rules on calculators.
How is compound interest different from simple interest?
In simple interest, interest is calculated on the original principal every period. In compound interest, interest is added to the principal at each compounding period, so later interest is calculated on a larger amount.
How do I solve annuity questions quickly?
First identify whether payments are at the end or start of each period. Then find the rate per period and the number of payments. Apply the matching formula and eliminate options that are clearly too large or too small.