Simple Interest
ICSE Class 7 · Mathematics · Chapter 10
What this chapter covers
- Principal, rate, time and interest
- Finding interest by the unitary method
- The simple interest formula
- Amount
- Finding the principal, rate or time
- Simple interest in daily life
Key definitions
Principal is the sum of money that is borrowed or lent.
Interest is the extra money paid by the borrower to the lender for the use of the principal.
Rate of interest is the interest charged on every ₹ 100 of principal for one year.
Time is the number of years for which the principal is borrowed or lent.
Simple interest is interest that is calculated every year on the original principal only.
Amount is the total money paid back at the end of the time, equal to the principal plus the interest.
Key points
- Principal (P) is the money borrowed or lent.
- Interest is the extra money paid for the use of the principal.
- Rate (R) is the interest on ₹ 100 for one year, written as a percentage per annum.
- Time (T) is the number of years for which the money is borrowed or lent.
- Simple interest is worked out on the original principal only, so it is the same every year.
- SI = (P × R × T)/(100), which comes straight from the unitary method.
- Amount = P + SI, and so SI = A - P.
- P = (SI × 100)/(R × T), R = (SI × 100)/(P × T) and T = (SI × 100)/(P × R).
- A rate given per month is multiplied by 12 to give the rate per annum.
- A sum doubles when the interest equals the principal.
- Check every answer by putting it back into the formula.
Questions answered
Arjun borrows money from a bank to buy a laptop. Who is the lender and who is the borrower?
The bank is the lender and Arjun is the borrower.
What does "9% per annum" mean?
It means that ₹ 9 of interest is charged every year on every ₹ 100 of principal.
Why is the interest the same every year under simple interest?
Simple interest is always worked out on the original principal, which never changes, so each year's interest is the same.
Find the simple interest on ₹ 7,500 at 4% per annum for 3 years.
SI = (7500 × 4 × 3)/(100) = 75 × 12 = ₹ 900.
Find the amount on ₹ 12,000 at 10% per annum simple interest for 2 years.
SI = (12000 × 10 × 2)/(100) = ₹ 2400, so A = 12000 + 2400 = ₹ 14,400.
A sum of ₹ 3,000 amounts to ₹ 3,840 in 4 years. Find the interest and the rate.
SI = 3840 - 3000 = ₹ 840. R = (840 × 100)/(3000 × 4) = 7, so the rate is 7% per annum.
What principal will earn ₹ 1,080 in 3 years at 9% per annum simple interest?
P = (1080 × 100)/(9 × 3) = (108000)/(27) = ₹ 4000.
In how many years will ₹ 6,000 earn ₹ 2,160 at 6% per annum simple interest?
T = (2160 × 100)/(6000 × 6) = (216000)/(36000) = 6 years.