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.

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.

Solution:
Interest from Tk. 2000 in 3 years at 5%:
SI = (P × R × T)/100
= (2000 × 5 × 3)/100
= 300 Tk.

Now,
Tk. 1500 to Produce the Same Interest (Tk. 300) at 4%:
Principal, P = Tk. 1500
Interest, SI = Tk. 300
Interest Rate, R = 4%
​ Time, T = ? years

SI = PRT/100
⇒ T = (SI × 100)/(P × R)
⇒ T = (300 × 100)/(1500 × 4)
⇒ T = 30000/6000
∴ T = 5 years