Question: What is the difference between simple and compound interest at 10% per annum on a sum of Tk. 5,000 at the end of 2 years?

Solution:
Principal (P) = Tk. 5,000
Rate (R) = 10% per annum
Time (T) = 2 years

Simple Interest (SI):
SI = (P × R × T)/100
= (5000 × 10 × 2) / 100
= 100000/100
= Tk. 1000

Compound Interest (CI):
Amount (A) = P × (1 + R/100)^T
= 5000 × (1 + 10/100)²
= 5000 × (1.1)²
= 5000 × 1.21
= Tk. 6050

∴ CI = A - P = 6050 - 5000
= Tk. 1050

∴ Difference between CI and SI = 1050 - 1000
= Tk. 50

Question: A certain principal amount, invested at simple interest, grows to Tk. 815 after 3 years and Tk. 854 after 4 years. What is the original principal amount?

Solution:
Given,
Amount after 3 years = Tk. 815
Amount after 4 years = Tk. 854
∴ Interest for 1 year = 854 - 815 = Tk. 39
∴ Interest for 3 years = 39 × 3 = Tk. 117
∴ Principal = 815 - 117 = Tk. 698

Question: The simple interest on a certain sum at 6% p.a. is Tk. 360 in 1 year. What will be the additional interest earned in 1 year if the rate increases to 7% p.a. on the same sum?

Solution:
Given,
Interest at 6% for 1 year:
Simple Interest, SI₁ = Tk. 360
Interest rate, R = 6%
Time, T = 1 year (initial)

We know,
SI₁ = PRT/100
⇒ 360 = (P × 6 × 1)/100
⇒ P = (360 × 100)/6
∴ P = Tk. 6000

So, the original sum (principal) is Tk. 6000.

Now,
Interest at 7% for 1 year:
SI₂ = PRT/100
⇒ SI₂ = (6000 × 7 × 1)/100
⇒ SI₂ = Tk. 420

Additional interest = SI₂ - SI_I
= 420 - 360
= Tk. 60