Question: What will be the total amount after 3 years if Tk. 1200 is invested at a simple interest rate of 5% annually?

Solution:
Here,
Principal, P = Tk. 1200
Rate of Interest, r = 5% = 5/100
Time, n = 3 years

We know,
Simple Interest, I = P × n × r
I = 1200 × 3 × (5/100)
I = 1200 × 3 × 5/100
I = 3600 × 5/100
I = 180 Tk.

Now, the Amount after 3 years, A = P + I
A = 1200 + 180
A = 1380 Tk.

∴ The amount after 3 years will be Tk. 1380.

Question: Tk. 1,000 becomes Tk. 1,200 in 4 years at a certain rate of simple interest. If the rate of interest is increased by 2%, what amount will Tk. 1,000 become in 4 years?

Solution:
Principal, P = 1000
Interest, I = 1,200 - 1,000 = 200
Time, T = 4 years

SI = PRT/100
⇒ R = (SI × 100)/(P × n)
⇒ R = (200 × 100)/(1000 × 4)
⇒ R = 20000/4000
⇒ R = 5

∴ Interest rate, R = 5%

∴ New Interest rate = 5% + 2% = 7%

New interest at 7% for 4 years:
New interest = (1,000 × 7 × 4)/100
= (28,000)/100
= 280 Tk.

New amount = Principal + Interest
= 1,000 + 280
= Tk. 1,280

Question: A bank offers 5% compound interest calculated half-yearly. A customer deposits Tk. 1600 on 1st January and another Tk. 1600 on 1st July of the same year. How much interest will he earn at the end of the year?

Solution:
Here,
Half-yearly interest rate = 5% ÷ 2 = (5/2)%

Now,
The first deposit of Tk. 1600 was made on 1st January.
It stays for 12 months, so it earns interest twice, once after 6 months, and again after 12 months.
So, it earns interest for 2 times (i.e., 2 half-years).

∴ A₁ = P(1 + r/100)ⁿ
= 1600 × {1 + 5/(2 × 100)}²
= 1600 × {1 + (1/40)}²
= 1600 × (41/40) × (41/40)
= 1600 × 1681/1600
= 1681

Now,
The second deposit of Tk. 1600 was made on 1st July.
It stays for 6 months, so it earns interest only once (1 half-year).

∴ A₂ = P(1 + r/100)ⁿ
= 1600 × (1 + 1/40)¹
= 1600 × (41/40)
= 1640

Total amount = 1681 + 1640 = 3321
Total money deposited = 1600 + 1600 = 3200
∴Interest earned = 3321 - 3200 = Tk. 121

∴ The customer would have gained Tk. 121 by way of interest.