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?
A
Tk. 129
B
Tk. 121
C
Tk. 118
D
Tk. 132
উত্তরের বিবরণ
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.
0
Updated: 1 month ago
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?
Created: 1 month ago
A
Tk. 40
B
Tk. 60
C
Tk. 70
D
Tk. 50
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
0
Updated: 1 month ago
The ratio of
milk and water in a solution is 7 : 4. After adding 8 liters of water, the
ratio of milk and water becomes 3 : 2. Find the final amount of water in the
solution.
Created: 1 month ago
A
48 liters
B
54 liters
C
56 liters
D
60 liters
Question: The ratio of milk and water in a solution is 7 :
4. After adding 8 liters of water, the ratio of milk and water becomes 3 : 2.
Find the final amount of water in the solution.
Solution:
Let the initial amount of milk = 7x liters
Let the initial amount of water = 4x liters
According to the question,
7x/(4x + 8) = 3/2
⇒
2 × 7x = 3 ×
(4x + 8)
⇒
14x = 12x + 24
⇒
14x - 12x = 24
⇒
2x = 24
⇒
x = 12
∴ Final amount of water = 4x + 8
= 4 × 12 + 8
= 48 + 8 = 56 liters
0
Updated: 1 week ago
In a business, the ratio of the capitals of A and B is 2 : 1, that of B and C is 4 : 3 and that of D and C is 6 : 5. What is the ratio of the capitals of A and D?
Created: 1 month ago
A
5 : 9
B
12 : 17
C
11 : 15
D
20 : 9
Question: In a business, the ratio of the capitals of A and
B is 2 : 1, that of B and C is 4 : 3 and that of D and C is 6 : 5. What is the
ratio of the capitals of A and D?
Solution:
Given,
A : B = 2 : 1 ⇒ A/B = 2/1
B : C = 4 : 3 ⇒ B/C = 4/3
D : C = 6 : 5 ⇒ C/D = 5/6
Now, A/D = (A/B) × (B/C) × (C/D)
= (2/1) × (4/3) × (5/6)
= 20/9
∴ A/D = 20 : 9
0
Updated: 1 month ago
