Compound Interest, Speed, Distance & Time
Compound Interest (Intro)
In simple interest the interest is the same each year. In compound interest the interest is added to the principal, so the next year's interest is calculated on a larger amount.
On ₹1000 at 10% for 2 years: year 1 interest = ₹100 (total ₹1100), year 2 interest = ₹110 (total ₹1210). So the compound interest is ₹210.
Example 1: Find the amount and CI on ₹1000 at 10% for 2 years.
Year 1: 1100; Year 2: 1210. Amount ₹1210, CI ₹210.
Example 2: What is the CI on ₹2000 at 10% for 1 year?
For 1 year CI = SI = ₹200.
Quick recap
- Compound interest is charged on the principal and on earlier interest.
- For 1 year, compound interest equals simple interest.
✓ Quick check
Compound interest is calculated on the principal and on the ___ ?
CI adds interest to the principal, so it is charged on earlier interest too.
What is the CI on ₹2000 at 10% for 1 year?
For 1 year, CI = SI = (2000 × 10 × 1) ÷ 100 = ₹200.
Speed, Distance & Time
Speed = distance ÷ time. Rearranging gives distance = speed × time and time = distance ÷ speed. A car covering 150 km in 3 hours travels at 50 km/hr.
Example 1: A car covers 150 km in 3 hours. Find its speed.
150 ÷ 3 = 50 km/hr.
Example 2: A car travels at 60 km/hr for 4 hours. Find the distance.
60 × 4 = 240 km.
Quick recap
- speed = distance ÷ time.
- distance = speed × time; time = distance ÷ speed.
✓ Quick check
A bus covers 120 km in 2 hours. What is its speed?
120 ÷ 2 = 60 km/hr.
A car travels at 50 km/hr for 3 hours. How far does it go?
50 × 3 = 150 km.
Average Speed & the Unitary Method
Average speed = total distance ÷ total time. The unitary method finds a single unit first: if a cyclist covers 90 km in 3 hours, the speed is 30 km/hr, so in 5 hours it covers 150 km.
Example 1: A car covers 240 km in 4 hours. What is its average speed?
240 ÷ 4 = 60 km/hr.
Example 2: How long does a 300 km journey take at 50 km/hr?
300 ÷ 50 = 6 hours.
Quick recap
- Average speed = total distance ÷ total time.
- Unitary method: find the per-hour rate first, then scale.
✓ Quick check
A car covers 240 km in 4 hours. What is its average speed?
240 ÷ 4 = 60 km/hr.
How long does a 300 km trip take at 50 km/hr?
300 ÷ 50 = 6 hours.
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