ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: A sum of 10,000 Taka is invested at 8% per annum. If the interest is compounded quarterly, the amount after 1 year will be:

Solution: 
The annual rate is 8%.
Since interest is compounded quarterly, the quarterly rate is:
8%/4 = 2% per quarter

Time period is 1 year, meaning there are 4 quarters.

We apply 2% interest every quarter.

First Quarter:
New Amount=10,000 + (2% of 10,000) = 10,000+200= 10,200

Second Quarter:
New Amount=10,200 + (2% of 10,200) =10,200+204= 10,404

Third Quarter:
New Amount=10,404 + (2% of 10,404) =10,404+208.08= 10,612.08

Fourth Quarter:
New Amount=10,612.08 + (2% of 10,612.08) =10,612.08+212.24= 10,824.32

So, The final amount after 1 year is 10,824 Taka.

Question: For three years, Tk 40,000 is invested at a 10% yearly interest rate. What is the difference between the Compound Interest (CI) and the Simple Interest (SI)?

Solution:
Given:
Principal (P) = Tk. 40,000
Rate of Interest (r) = 10% per annum
Time (n) = 3 years

Simple Interest, I = Pnr
= 40000 × 3 × (10/100)
= 12000

Compound Principal = P × (1 + r)ⁿ
= 40000 × (1 + (10/100))³
= 40,000×(1.1)³
= 53240

Compound Interest, C = 53240−40000 = 13240

So, Difference = 13240 - 12000 = 1240 Taka

Question: A sum of Taka 50,000 is invested at 6% simple interest for the first 3 years and 8% compound interest for the next 2 years. What is the total amount after 5 years?

Solution: 
Given,
Tk. 50,000 is invested.
6% simple interest for the first 3 years.
8% compound interest for the next 2 years.

Simple Interest, I = Pnr
= 50000 × 3 × (6/100)
= 9000

New Principal = 50,000 + 9,000 = 59,000

Compound Principal = P × (1 + r)ⁿ
= 59000 × (1 + (8/100))²
= 59000 × (1.08)²
= 68,817.60

Question: If the simple interest on a sum of money is 40% of the principal over 8 years, what is the annual interest rate?

Solution: 
We know, Simple Interest, I = Pnr

Given, 
Simple Interest = 0.4 × Principal (since 40% of the principal)
= 0.4 × P

Where, Principal = P
Rate = r
Time, n = 8 years

So, 0.4 × P = P × 8 × r
⇒ r = 0.4/8
⇒ r = 0.05 × 100%
∴ r = 5%

Question: The compound interest on Taka 12,000 for 2 years at 10% per annum compounded half-yearly is -

Solution: 
Given, 
P = 12,000 (Principal)
r = 10% = 0.1
Compounded half-yearly means, n = 2
Time, t = 2 years

Compound Interest = A - P
= 14586 - 12000
= 2586 Taka

Question: Find the simple interest on BDT 8,000 at 6% per annum for 9 months.

Solution: 
Given, P = 8000 Taka
n = 9 months = 0.75 years
r = 6% 

Simple Interest, I = Pnr
= 8000 × 0.75 × 6/100
= 80 × 4.5
= 360 Taka

Question: The compound interest on Tk. 10,000 at 10% per annum for a certain period is Tk. 2,100. The time period (in years) is -

Solution: 
Principal amount, P = 10,000 taka
Compound Interest, I = 2100 taka

So, Total amount, A = 12100 Taka
r = 10% = 0.1

Now, (1.1)² = 1.21
So, n = 2 (Time period)

Question: If a sum of BDT 5,000 becomes BDT 6,728 in 2 years at compound interest, what is the rate of interest per annum?

Solution: Given, 
A = Amount after interest = BDT 6,728
P = Principal amount = BDT 5,000
r = Rate of interest per annum 
n = Time in years = 2

Thus, the rate of interest per annum is 16%.

Question: A sum of money invested at compound interest triples itself in 3 years. In how many years will it become 27 times itself?

Solution:
Since the sum triples in 3 years, we can write:

Thus, it will take 9 years for the amount to become 27 times itself.

Question: If the simple interest on 6,000 Taka for 3 years is 1,800 Taka, what is the rate of interest per annum?

Solution:
Given, I = 1,800 Taka
P = 6,000 Taka
n = 3 years

We know, 
I = Pnr
⇒ r = I/Pn
⇒ r = 1800/(6000×3)
⇒ r = 0.1
∴ r = 10%

Question: The simple interest on a certain sum of money at 4% per annum for 3 years is 1,200 Taka. The compound interest on the same sum for the same period and at the same rate is - 

Solution: 
Given, Simple Interest, I = 1,200 Taka
r = 4% = 0.04
n = 3 years

We know,
I = Pnr
P = I/nr
P = 1200/(3×0.04)
P = 10,000 Taka

For Compound Interest, 

So, Compound Interest = 11248.64 - 10000 
= 1248.64 Taka
= 1249 Taka

Question: If 6,250 Taka is invested at 12% simple interest, how much time will it take for the interest to reach 3,000 Taka?

Answer: 
Given, 
P = 6250 Taka
I = 3000 Taka
r = 12% = 0.12
Time = n

We know,
I = Pnr
n = I/Pr
n = 3000/(6250×0.12)
n = 4 years

Question: A sum of 12,000 Taka is lent out in two parts. One part is lent at 8% simple interest and the other at 10% simple interest. If the total annual interest is 1,080 Taka, how much is lent at 8%?

Solution:
Let, 
Amount lent at 8% simple interest = x
Amount lent at 10% simple interest = (12000 - x)

We know,
I = Pnr
I = Pr [Since the time is 1 year]

Interest from the amount lent at 8%, 
I = x(8/100) = 0.08x

Interest from the amount lent at 10%, 
I = (12000 - x) × (10/100) = 0.10(12,000−x)

ATQ,
0.08x + 0.10(12,000−x) = 1080
⇒ 0.02x = 120
∴ x = 6000 Taka

So, Amount lent at 8% simple interest = 6000 Taka