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class 8 ganita prakash chapter 1
📖 Textbook Theory: Interest & Compounding
Interest is the extra money paid by institutions (like banks) on money deposited with them. The original money deposited is called the Principal.
p.a. stands for "per annum", meaning "per year". A 10% p.a. rate means the bank gives you 10% of your Principal every year.
The Big Difference:
No Compounding (Simple): The interest is paid out and leaves the account. The Principal stays exactly the same every year.
Compounding: The interest is added back into the account. Next year, you earn interest on the Principal PLUS the old interest! It snowballs.
Example 7: If one deposits ₹6000 in the bank at 10% p.a., what is the total amount received after 3 years?
1
No Compounding (Simple Interest): The 10% is calculated ONCE on the original ₹6000. It stays exactly the same every year.
2
With Compounding: The 10% is calculated on the new, updated balance at the end of each year. Year 2 calculates 10% of ₹6600, not ₹6000.
1
Option 1: 10% of 6000 is 600. Add 600 for Year 1, 600 for Year 2, and 600 for Year 3.
2
Option 2: Yr 1 = 6000 + 10%. Yr 2 = 6600 + 10%. Yr 3 = 7260 + 10%.
!
The "Multiply by 3" Trap: For Option 2 (Compounding), you cannot just multiply the interest by 3. $600 \times 3 = 1800$. That is Simple Interest! Compounding must be calculated step-by-step because the base changes every year.
Option 1: No Compounding
| Year | Amount in FD | Interest Returned (10%) |
|---|---|---|
| Year 1 | ₹6000 | $0.10 \times 6000 =$ ₹600 |
| Year 2 | ₹6000 | $0.10 \times 6000 =$ ₹600 |
| Year 3 | ₹6000 | $0.10 \times 6000 =$ ₹600 |
| Total | Principal (6000) + Interest (1800) = ₹7800 | |
Option 2: With Compounding
| Year | Amount in FD (New Base) | Interest Added (10%) |
|---|---|---|
| Year 1 | ₹6000 | $0.10 \times 6000 =$ ₹600 |
| Year 2 | ₹6600 (6000+600) | $0.10 \times 6600 =$ ₹660 |
| Year 3 | ₹7260 (6600+660) | $0.10 \times 7260 =$ ₹726 |
| Total | Final Amount in FD = ₹7986 | |
Priya deposits ₹10,000 in a scheme that offers 10% p.a. interest for 2 years.
Calculate the total final amount she will receive if:
(A) The interest is NOT compounded (Simple Interest).
(B) The interest IS compounded annually.
Calculate the total final amount she will receive if:
(A) The interest is NOT compounded (Simple Interest).
(B) The interest IS compounded annually.
1
This mirrors Example 7 perfectly, just for 2 years instead of 3. Follow the tables!
1
Part A: 10% of 10,000 is 1000. She gets 1000 in year 1, and 1000 in year 2.
2
Part B: Yr 1 interest is 1000. Add it to the base. Yr 2 base is now 11,000. Calculate 10% of 11,000.
!
Do not forget to add the final interest back to the base to get the Total Amount. The question asks for the Total Amount, not just the interest earned.
Step-by-Step Calculation
Part (A): No Compounding
Yr 1 Interest = 10% of 10,000 = 1000.
Yr 2 Interest = 10% of 10,000 = 1000.
Total Amount = $10,000 + 1000 + 1000 =$ ₹12,000.
Part (B): Compounding
Yr 1 Interest = 10% of 10,000 = 1000. (New Base = 11,000).
Yr 2 Interest = 10% of 11,000 = 1100.
Total Amount = $11,000 + 1100 =$ ₹12,100.
Ans: (A) ₹12,000 (B) ₹12,100
In Option 2 (Compounding) from the textbook example, why does the interest earned increase from ₹600 in Year 1 to ₹660 in Year 2?
A. Because the bank increased the interest rate from 10% to 11%.
B. Because time is a multiplier, so Year 2 automatically gets more.
C. Because the ₹600 earned in Year 1 was added to the Principal. The 10% rate is now acting on a larger base (₹6600 instead of ₹6000).
D. Because compounding is magic.
1
"Compounding" literally means adding the interest back into the main pot.
1
Look at the table for Option 2. What happens to the "Amount in FD" at the start of Year 2?
!
The percentage rate (10%) never changes. What changes is the number that the 10% is being multiplied by.
Logical Explanation
In compounding, you earn "interest on your interest."
In Year 1, you earned ₹600. That ₹600 was locked into the account.
In Year 2, the bank pays you 10% on the original ₹6000 (which is ₹600) AND 10% on the new ₹600 (which is ₹60). Total = ₹660.
Ans: Option (C)
In the context of bank interest, what does the abbreviation "p.a." stand for, and what does it mathematically mean?
A. "Principal Amount" - it means the percentage is calculated on the principal.
B. "Per Annum" - it means the interest rate is applied once per year.
C. "Percentage Added" - it tells you to add the percentage to the base.
D. "Per Account" - it means the rate applies to the whole account.
1
This is a direct vocabulary definition from the textbook.
Vocabulary Check
The textbook explicitly defines this on Page 21:
"'p.a.' is the short form of per annum, which means for every year."
It establishes the time frame for the percentage. 10% p.a. means you must wait 12 months to receive the full 10% growth.
Ans: Option (B)
