What will be the compound interest and compound amount of Rs.
2,000 at the interest rate of 12% p.a. in 2 years? Find the
compound interest without using formula.
Solution:
Given information:
Principal (P1)=Rs. 2,000
Rate of interest (R)=12% p.a.
Time (T)=2 years
Step 1: Calculate interest for the first year
At the end of the first year, simple interest (I1)=100P1TR
I1=1002000×1×12=Rs. 240
Step 2: Find principal for the second year
Principal for the second year (P2)= Amount at the end of the
first year
P2=P1+I1=Rs. (2000+240)=Rs. 2,240
Step 3: Calculate interest for the second year
Again, simple interest for the second year (I2)=100P2TR
I2=1002240×1×12=Rs. 268.8
Step 4: Calculate total compound interest
Thus, the compound interest at the end of 2 years:
CI=I1+I2=240+268.8=Rs. 508.8
Step 5: Calculate compound amount
Compound amount (CA)=P1+CI
CA=2000+508.8=Rs. 2,508.8
Final Answers:
Compound Interest = Rs. 508.8
Compound Amount = Rs. 2,508.8
Verification:
We can verify this by checking that the compound amount equals the
principal plus all accumulated interest:
2,000+240+268.8=2,508.8 ✓
📺 View YouTube Video
Question 2
Find the compound interest and compound amount of the borrowed
amount of Rs. 25,000 which is paid in exactly 3 years at the
rate of yearly compound interest rate 12%.
A man borrowed Rs. 32,000 from his friend at the rate of simple
interest of 12.5% per annum. He lent the whole sum to a
shopkeeper at the same rate of compound interest. How much more
money will he get in 3 years? Find.
Sameer decided to invest Rs. 5,000 at the rate of 8% per annum
for 2 years. For this, he has two safe alternatives. The first
alternative is to get half yearly compound interest and the
second alternative is to get yearly compound interest. If you
were to suggest him, which alternative would you suggest? Write
with reason.
The difference between half yearly compound interest and yearly
compound interest is given by:
CI1−CI2=Rs. 849.29−Rs. 832=Rs. 17.29
Conclusion:
Since half yearly compound interest is Rs. 17.29 more than yearly
compound interest,
I would suggest him to invest in the first alternative
(half-yearly compounding).
Reason: When interest is compounded more
frequently (half-yearly vs yearly), the effective return is higher
because interest is calculated and added to the principal more
often, leading to a compounding effect on the interest itself.
Summary:
Half-yearly compound interest = Rs. 849.29
Yearly compound interest = Rs. 832.00
Extra benefit with half-yearly = Rs. 17.29
📺 View YouTube Video
Question 5
A twelve-grade student invests Rs. 10,000 for 2 years at the
rate of yearly compound interest. If the compound interest in 1
year is Rs. 1,200
Find the rate of yearly compound interest.
Find the yearly compound amount at the end of the second year.