1. What will a loan of ₹15,000 amount to in 3 years if compounded annually at the rate of 10% p.a?
Solution:
compound interest: Amount = P (1 + R/100)^T
Where:
P = Principal (starting amount) = ₹15,000
R = Rate of interest per year = 10%
T = Time in years = 3
Amount = 15000 × (1 + 10/100)³
= 15000 × (1 + 0.10)³
= 15000 × (1.10)³
= 15000 × 1.331
= ₹19,965Answer: The loan amount will be ₹19,965.
2. Find the difference between compound interest and simple interest on a sum of ₹12,000 at the rate of 12% p.a. for 2 years (compounded annually).
Solution:
Calculate Simple Interest (SI)
SI = (P × R × T) / 100
= (12000 × 12 × 2) / 100
= ₹2,880
Calculate Compound Interest (CI)
First, find the Amount (A).
A = P (1 + R/100)^T
= 12000 × (1 + 12/100)²
= 12000 × (1.12)²
= 12000 × 1.2544
= ₹15,052.80
Now, CI = Amount – Principal
= 15052.80 – 12000
= ₹3,052.80
Find the Difference
Difference = CI – SI
= 3052.80 – 2880
= ₹172.80
Answer: The difference is ₹172.80.
3. Find the compound interest on ₹5000 at the rate of 10% p.a. compounded semi-annually for 1 ½ years.
Solution:
SI = (12000 × 12 × 2)/100 = ₹2,880
Amount = 12000 × (1 + 12/100)^2 = 12000 × (1.12)^2 = 12000 × 1.2544 = ₹15,052.80
CI = Amount – Principal = 15052.80 – 12000 = ₹3,052.80
Difference = CI – SI = 3052.80 – 2880 = ₹172.80
Answer: ₹172.80
Find the difference between compound interest and simple interest on a sum of ₹64,000 at the rate of 20% p.a. compounded semi-annually for 1 ½ years.
Solution:
Simple Interest (SI) for 1.5 years
SI = (P × R × T) / 100
= (64000 × 20 × 1.5) / 100
= (64000 × 30) / 100
= ₹19,200
Compound Interest (CI) compounded semi-annually
P = ₹64000
Annual Rate = 20%, so Semi-annual Rate = 20%/2 = 10% per half-year
Time = 1.5 years = 3 half-years
A = P (1 + R/100)^T
= 64000 × (1 + 10/100)³
= 64000 × (1.10)³
= 64000 × 1.331
= ₹85,184
CI = Amount – Principal
= 85184 – 64000
= ₹21,184
Find the Difference
Difference = CI – SI
= 21184 – 19200
= ₹1,984
Answer: The difference is ₹1,984.