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
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: 4 weeks ago
How many years will Tk. 1500 need at 4% simple interest to earn the same interest as Tk. 2000 earns in 3 years at 5% simple interest?
Created: 4 weeks ago
A
4 years
B
5 years
C
6 years
D
8 years
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
0
Updated: 4 weeks ago
In how many years will Tk. 750 amount to Tk. 900 at 4% simple interest per annum?
Created: 4 weeks ago
A
3.5 years
B
3 years
C
4.5 years
D
5 years
Solution:
Simple Interest = Amount - Principal
= 900 - 750
= 150
Here,
Principal, P = 750
Interest Rate, R = 4%
SI = 150
Time, T = ?
SI = PRT/100
⇒ T = (SI × 100)/(P × R)
= (150 × 100)/(750 × 4)
= 15000/3000
= 5 years
0
Updated: 4 weeks ago
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?
Created: 4 weeks ago
A
Tk. 60
B
Tk. 80
C
Tk. 70
D
Tk. 100
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 - SII
= 420 - 360
= Tk. 60
0
Updated: 4 weeks ago
