ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: If simple interest on a certain sum of money is Tk. 400 and the rate of interest per annum equals the number of years, then the rate of interest is-

Solution:
Let,
The rate of interest is x%
∴ Number of years is x

The interest of 1 year of 100 taka is x
∴ The interest of x years of 100 Taka is x × x = x²

ATQ,
x² = 400 
∴ x = 20

∴ The rate of interest is 20%

Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk. 12,000 after 3 years at the same rate?

Solution: 
Let,P = Tk.100
Then, I = Tk. 60
and, T = 6years
we know,
I = Pnr/100
r = (I × 100)/Pn
= (60 × 100)/ (100 × 6)
= 10%

the compound principle of Tk. 12,000 after 3 years at the same rate wii be
C = P(1 + r)n
= 12000 ( 1 + 10/100)3
= 12000 ( 11/10)3
= 12000 (1331/1000)
= 12 × 1331
= 15972
∴ compound interest will be = (15972 - 12000)
= 3972 Tk.

Question: In what time will the simple interest on 1200 Tk. at 4% per annum be the same as that on 600 Tk. at 8% per annum in 2 years?

Solution: 
the interest of 600 Tk. at 8% per annum in 2 years is = 600 × 2 × 8%
= 96 Tk.

let, the time is n years.
I = 96 Tk.
P = 1200 Tk.
r = 4%

as we know,
I = Pnr
n = I / Pr
= 96 / (1200 × 4%)
= 2 years

Question: The compound interest on 15000 at 10% per annum is 3150 Tk. What is the time period?

Solution: 
Let the time is = n
C = 15000 + 3150 
= 18150 Tk.
r = 10%

we know,
 C = P(1 + r)ⁿ
⇒18150 = 15000(1 + 1/10)ⁿ
⇒ 18150/15000 = (11/10)ⁿ
⇒ 121/100 = (11/10)ⁿ
⇒ (11/10)² = (11/10)ⁿ
⇒ n = 2

Question: A certain amount of money becomes 3 times in 12 years. What is the interest rate?

Solution:
let the principle amount it X.
so, the Interest = 3X -X = 2X
time, n = 12 years
 let,
rate = r%

As we know,
I = Pnr/100
r = (I × 100)/Pn
= (2X × 100)/ 12X
= 16.67%

Question: What will be the simple interest earned on an amount of Tk. 16,000 in 9 months at the rate of 25/4% p.a. ?

Solution:
here, 
P = 16000
n = 9/12 years = 3/4
r = 25/4%

we know,
I = Pnr
= 16000 × 3/4 × 25/4%
= 750

Question: On a sum of money, the simple interest for 2 years is Tk. 880, while the compound interest is Tk. 928.4, the rate of interest being the same in both cases. The rate of interest is -

Solution:
Difference of Compound interest and Simple interest for 2 years = Tk. (928.4 - 880) = Tk. 48.4
Simple interest for 1 years = 880/2 = Tk. 440

Simple interest on 440 for 1 year = 48.4
Interst rate = {(48.4 × 100)/440}% = 11%

Question: What sum of money will amount to Tk. 1500 in 5 years and to Tk. 1620 in 7 years at simple interest?

Solution:
in two years the interest becomes = 1620 - 1500 = 120Tk.
in 5 years, interest = (120/2)/5 =300 Tk.

so , the principle amount is = 1500 - 300 = 1200 Tk.

Question: What will be the compound interest of Tk. 3500 in 2 years at 20% per annum if the interest is compounded half - yearly?

Solution: 
P =3500
r = 20% = 10% half - yearly
n = 2 years = 4 half - yearly

we know,
C = P(1 + r)ⁿ
= 3500 ( 1 + 10/100)⁴
= 3500 (11/10)⁴
= 5124.35
∴ compound interest = 5124.35 - 3500 = 1624.35 Tk.

Question: Rakib invested 10000 Tk. in two 5 years term. He received 5% for the first term and 8% for the second term. What is the average rate of interest did he received?

Solution:
in first term, he received = 10000 × 5 × 5%
= 2500 Tk.
in second term, he received = 10000 × 5 × 8%
= 4000 Tk.
so,
total interest after 10 years, I = 6500
P = 10000
n = 10
r = ?

we know,
I = Pnr/100
r = 100I / Pn
= 650000/(10000 × 10)
= 6.5%

Question: Puja invested 50000 for 2 years at 15% compound rate. What is the simple interest rate that she needs to put the same amount for the same time to ensure the same amount of return?

Solution: 
P = 50000
n = 2 years 
r = 15%

C = p(1 + r)ⁿ
= 50000(1 + 15/100)²
= 50000 ( 115/100)²
= 66125

return = 66125 - 50000 = 16125Tk

Let the simple interest rate is X%
we know, 
I = PnX/100
X = (100 × I)/ Pn
= (100 × 16125)/(50000 × 2)
= 16.125%

Question: If a sum doubles in 12 years, how much will it be in 8 years ?

Solution:
let the rate is r
we know,
I = Pnr/100
r = (I × 100)/Pn
= (P × 100)/(P × 12)
= 100/12 %

in 8 years,
I = Pnr/100
= (P × 8 × 100/12)/100
= 2P/3
= 2/3 of P

It will be (1 + 2/3) = 5/3P

Question: A company increases salary of an officer at 15% per year. In 2024 an employee receives 28500. what was his salary in 2022?

Solution: 
let, his saray in 2022 was 100 Tk.
at 15% increment,
salary of 2023 is = 100(1 + 15/100)
= 115 Tk.
salary of 2024 is = 115(1 + 15/100)
=  132.25
∴ his salary in 2022 was = (28500 × 100)/ 132.25
= 21550 Tk.

Question: A sum of money invested at simple interest becomes 23/10 of itself in 2 years and 6 months. What is the rate of interest per annum?

Solution: 
let,
principle = P
interest, I = (23P/10 - P)
= 13P/10
time, n =  2 years 6 months
= 2.5 years
we know,
I = Pnr/100
r = (100 × I)/Pn
= (100 × 13P/10) /P × 2.5
= 52%