Simple and Compound Interest
ICSE Class 8 · Mathematics · Chapter 9
What this chapter covers
- Borrowing, lending and the words of interest
- Simple interest: a recap
- What compound interest means
- Compound interest year by year
- Arriving at the formula through a pattern
- Compound interest compounded half-yearly
- The difference between simple and compound interest
- Interest in daily life
Key definitions
Principal is the money that is borrowed from a lender or deposited in a bank at the start.
Interest is the extra money that a borrower pays to a lender for the use of the lender's money.
Rate of interest is the interest charged on every ₹100 of principal for one year, written as a percentage.
Time is the period for which the money is borrowed or deposited.
Amount is the total money at the end of the time, that is, the principal plus the interest, whether it is paid back on a loan or received on a deposit.
Simple interest is interest that is calculated on the original principal only, for the whole period of the loan.
Compound interest is interest that is calculated on the principal together with all the interest already added to it.
The conversion period is the fixed length of time after which the interest earned is added to the principal.
Key points
- Principal is the money borrowed or deposited; amount = principal + interest.
- Simple interest is worked out on the original principal only: SI = (P × R × T)/(100).
- From the SI formula you can find any one of principal, rate or time when the other three are known.
- Compound interest is worked out on the principal plus the interest already added to it.
- The step method finds compound interest one period at a time; each amount becomes the next principal.
- The pattern of the steps gives A = P(1 + (R)/(100))n and CI = A - P.
- For half-yearly compounding, halve the yearly rate and double the number of years.
- For the first year compounded yearly, CI equals SI; after that, CI is always greater.
- For 2 years, CI − SI is the interest on one year's interest, P × (R)/(100) × (R)/(100).