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: 8 hours ago
The ratio of the present ages of a mother and son is 7 : 2. After 7 years, the ratio of their ages becomes 8 : 3. What will be the ratio of their ages after 11 years?
Created: 8 hours ago
A
12 : 5
B
12 : 7
C
10 : 7
D
13 : 6
Question: The ratio of the present ages of a mother and son
is 7 : 2. After 7 years, the ratio of their ages becomes 8 : 3. What will be
the ratio of their ages after 11 years?
Solution:
Let,
The present age of the mother = 7x years
The present age of the son = 2x years
After 7 years, their ages will be:
Mother = (7x + 7) years
Son = (2x + 7) years
According to the question,
(7x + 7)/(2x + 7) = 8/3
⇒
3(7x + 7) = 8(2x + 7)
⇒
21x + 21 = 16x + 56
⇒
21x - 16x = 56 - 21
⇒
5x = 35
⇒
x = 35/5
∴
x = 7
Present age of mother = 7 × 7 = 49 years
Present age of son = 2 × 7 = 14 years
Now, after 11 years,
Mother's age = 49 + 11 = 60 years
Son's age = 14 + 11 = 25 years
∴ The ratio of their ages after 11 years,
= 60 : 25
= 12 : 5
0
Updated: 8 hours ago
A sum of Tk. 30,000 yields a compound interest of Tk. 4347 when invested at 7% per annum. What is the investment period in years?
Created: 8 hours ago
A
2 years
B
4 years
C
3 years
D
5 years
Question: A sum of Tk. 30,000 yields a compound interest of
Tk. 4347 when invested at 7% per annum. What is the investment period in years?
Solution:
Given,
Principal, P = 30000
Rate, r = 7% per annum
Compound Interest, CI = 4347
We know,
Amount, A = P + CI = 30000 + 4347 = 34347
Using the compound amount formula:
A = P(1 + r/100)n
⇒
34347 = 30000 × (1 + 7/100)n
⇒
34347 = 30000 × (107/100)n
⇒
(107/100)n = 34347/30000
⇒
(1.07)n = 1.1449
⇒
(1.07)n = (1.07)2
∴
n = 2 years
0
Updated: 8 hours ago
The simple interest on a sum of money is Tk. 720 in 12 years. If the principal is doubled after 6 years, what will be the total interest at the end of 12 years?
Created: 8 hours ago
A
Tk. 720
B
Tk. 900
C
Tk. 1480
D
Tk. 1080
Question: The simple interest on a sum of money is Tk. 720
in 12 years. If the principal is doubled after 6 years, what will be the total
interest at the end of 12 years?
Solution:
সরল সুদ সময়ের সাথে
সমানভাবে অর্জিত হয়। যদি 12 বছরে
720 টাকা সুদ পাওয়া যায়,
তাহলে 6 বছরে (অর্থাৎ অর্ধেক সময়ে) মোট সুদের অর্ধেক
পাওয়া যাবে।
∴ প্রথম
6 বছরের সুদ = মোট সুদের অর্ধেক
= 720/2 = 360 টাকা
পরবর্তী
6 বছরে মূলধন দ্বিগুণ করা হলে, সুদও
দ্বিগুণ হবে।
∴
পরবর্তী 6 বছরের সুদ = 360 × 2 = 720 টাকা
∴ মোট
সুদ = প্রথম 6 বছরের সুদ + পরবর্তী 6 বছরের সুদ
= 360 + 720 = 1080 টাকা
0
Updated: 8 hours ago
