Compound Interest [Basic Concepts]
ICSE Class 9 · Mathematics · Chapter 2
What this chapter covers
- Interest, principal and amount
- Simple interest as the starting point
- The idea of compound interest
- Computing the amount and compound interest for 2 years
- Computing the amount and compound interest for 3 years
- Different rates of interest in different years
- Interest for a particular year
- Comparing compound interest with simple interest
- Repaying part of a loan
- Working back from year-by-year figures
- Common mistakes and how to avoid them
Key definitions
Principal is the sum of money that is lent, borrowed or deposited at the start, and it is written P.
Interest is the extra money paid by the borrower to the lender for the use of the principal over a period of time, and it is written I.
Amount is the total sum due at the end of a period, equal to the principal plus the interest for that period, so that A = P + I.
Rate of interest is the interest charged on every ₹100 for one year, written as a percentage per annum (p.a.) and denoted by R or r.
Simple interest is the interest calculated on the original principal only, for the whole period, so that the same interest is earned in every year.
Compound interest is the interest calculated on a principal that grows at the end of every conversion period, because the interest of each period is added to the principal to form the principal for the next period.
The conversion period is the fixed interval of time at the end of which the interest is added to the principal; when the interest is added once every year, the interest is said to be compounded annually.
Key points
- Amount = principal + interest, and the rate of interest is the interest on ₹100 for one year.
- Simple interest is always worked out on the original principal, so it is the same every year.
- Compound interest is repeated simple interest for one year at a time, with a principal that grows each year.
- When interest is compounded annually, the amount at the end of each year becomes the principal for the next year.
- Compound interest for the whole period = final amount − original principal.
- Keep paise in every year's working and round only at the end.
- When rates differ from year to year, apply each year's rate to that year's principal.
- The interest for a particular year is one year's interest on the principal at the start of that year.
- With a constant rate, each year's interest is R% more than the previous year's interest.
- Compound interest equals simple interest for the first year and is larger after that; the extra is interest on interest.
- A part repayment at the end of a year is subtracted from the amount due, and the remainder is the next year's principal.
- Two consecutive amounts, or two consecutive yearly interests, are enough to find the rate and the original sum.
Questions answered
Define compound interest.
What is meant by "interest compounded annually"?
Find the amount and the compound interest on ₹4,000 for 2 years at 5% per annum.
Find the compound interest on ₹9,000 for 3 years at 10% per annum.
Find the compound interest on ₹2,500 for 3 years at 4% per annum.
₹30,000 is invested at compound interest, the rate being 6% for the first year and 10% for the second year. Find the amount at the end of 2 years.
Find the difference between the compound interest and the simple interest on ₹8,000 for 2 years at 15% per annum.
Why is compound interest never less than simple interest for the same principal, rate and time?
Past board exam questions
ICSE 2019 sample paper · 3 marks
Mr. Ravi borrows ₹ 16,000 for 2 years. The rate of interest for the two successive years are 10% and 12% respectively. If he repays ₹ 5,600 at the end of first year, find the amount outstanding at the end of the second year.
Show answer
ICSE 2019 sample paper · 4 marks
A sum of ₹ 12,500 is deposited for 1½ years, compounded half yearly. It amounts to ₹ 13,000/- at the end of first half year. Find: (i) The rate of interest (ii) The final amount. Give your answer correct to the nearest rupee.