ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Let Principle = P.
Then, S.I = 2P and T = 20 years
∴ Rate = {(100 × 2P)/(P × 10)}
Now, principle = P, S.I. = P, R = 10%

∴ Time = {(100 × P)/(P × 10)} yrs
= 10 yrs.

Let the amount invested in scheme A be Tk. x and that in B be Tk. 3x.
Then,
Then,
{(x × 4 × 8)/100 + (3x × 2 × 13)/100} = 1320
⇒ 32x/100 + 78x/100 = 1320
⇒ 110x/100 = 1320
⇒ x = (1320 × 100)/110
⇒ x = Tk. 1200

Hence, Tk. 1200 was invested in scheme A.

Given that,
P = Rs 50,000
R = 3.5%
T = 3 years

S.I.
= (P × R × T)/100
= (50,000 × 3.5 × 3)/100
= Tk. 5250.

Interest charged on Tk 10,000 is,
(15/100) × 10000 = Tk. 1500

Interest for two years =
Tk. 1500 × 2 = Tk. 3000

The amount payable after two years = principal + interest
= Tk. 10000 + Tk. 3000 = Tk. 13000

Let,
The amount invested at 12% be Tk. x and that invested at 10% be Tk. y
Then, 12% x + 10% of y = 130
⇒ 12x + 10y = 13000
⇒ 6x + 5y = 6500 .............(i)

And, 10% x + 12% of y = 134
⇒ 10x + 12y = 13400
⇒ 5x + 6y = 6700 .......(ii)

Adding (i) and (ii) we get,
11(x + y) = 13200
⇒ x + y = 1200 ..........(iii)

Subtracting (i) from (ii) we get,
x + y = 200 .........(iv)

Adding (iii) and (iv) we get,
2y = 1400
⇒ y = 700

∴ x = 1200 - 700 = 500

So,
The amount invested at 12% is TK 500
And the amount invested at 10% is TK 700.

Total price of TV = Tk. 16000
Initial payment = Tk. 4000
Remaining amount = Tk. 12000
Simple interest in 15 months for Tk. 12000

S.I. = (P × R × T)/100
= ( 12000 × 12 × 15)/(100 × 12)
= Tk. 1800

⇒ With S.I. total amount to be paid for principal amount Tk. 12000
= Tk. (12000 + 1800)
= Tk. 13800

Therefore,
total amount he pays for the TV is
= 4000 + 13800
= Tk. 17800

Two parts are = A and (40800 - A)
Time period and Simple interest are same for both

Simple Interest = (P × R × T)/100

∴ (A × 6.25 × 8)/100 = {(40800 - A) × 7 × 5}/100
∴ 50A = 35 × 40800 - 35A
∴ 85A = 35 × 40800
∴ A = 8400

Smaller amount is Tk. 16800
By direct observation, we can say that 16800 is smaller - as it is smaller than half of 40800.

Let Sum = Tk. x. Then, S.I. = Tk. x, Time = 16 years
Rate = {(100 × x)/(x × 16)}%
= (25/4)%
= 6(1/4)%

Now,
Sum =Tk. x,
Time = 8 years
Rate = 6(1/4)%

∴ S.I. = Tk. {(x × 25 × 8)/(100 × 4)}
= Tk. x/2
So, amount = Tk. (x + x/2)
= Tk. 3x/2
= 1(1/2) times

Let Simple Interest be S
Original sum 'P' and Time 'T' remains the same
Also, 3% increase in rate of interested means, New rate = 15%
Increase of 300 Rs/- in the final amount means, New amount = Tk. 3300/-

So, Amount 2 - Amount 1 = (P + S₁) - (P + S₂) = S₁ - S₂
∴ 3300 - 3000 = S₁ - S₂
∴ S₁ - S₂ = 300

∴ {(P × R × T)/100} - {(P × 12 × T)/100 = 300
3PT/100 = 300
PT = 10000
For R = 15%,

Simple interest = (P × 15 × T)/100
= (10000 × 15)/100
= Tk. 1500

Original sum = Amount - Interest = 3300 - 1500 = Tk. 1800 (Principle amount)

Also, PT = 10000
T = 10000/1800
= 5.55 years.

Total cost of the computer = Tk. 39000
Down payment = Tk. 17000
Balance = Tk. (39000 - 17000) = Tk. 22000.
Let the rate of interest be R% p.a.
Amount of Tk. 22000 for 5 months
= {22000 + 22000 × (5/12) × R/100}
= {22000 + (275R/3)}

The customer pays the shopkeeper Tk. 4800 after 1 month,
Tk. 4800 after 2 months, ...... and Tk. 4800 after 5 months.

Thus, the shopkeeper keeps Tk. 4800 for 4 months, Tk. 4800 for 3 months, Tk. 4800 for 2 months, Tk. 4800 for 1 months and Tk. 4800 at the end.

∴ sum of the amounts of these installments
= (Tk. 4800 + S.I. on Tk. 4800 for 4 months) + (Tk. 4800 + S.I. on Tk. 4800 for 3 months) + ...... + (Tk. 4800 + S.I. on Tk. 4800 for 1 month) + Tk. 4800
= Tk. (4800 × 5) + S.I. on Tk. 4800 for (4 + 3 + 2 + 1) months
= Tk. 24000 + S.I. on Tk. 4800 for 10 months
= 24000 × 4800 × R × (10/12) × (1/100)
= (24000 + 40 R)

∴ {22000 + (275R/3)} = (24000 + 40 R)
⇒ 155R/3 = 2000
⇒ R = (2000 × 3)/155
= 38.71

Principle,
= (P.W. of Tk. 882 due 1 year hence) + (P.W of Tk. 882 due 2 years hence)
= [{882/(1 + 5/100)} + {882/(1 + 5/100)²}]
= [{(882 × 20)/21} + {(882 × 400)/441}]
= Tk. 1640.

Principle = P
Compound Interest = Total amount - Principle
P = P(1 + R/100]ⁿ - P

Simple interest = PRT/100
R= 25% per annum; T and n = 3 years
Compound Interest - Simple Interest = Tk. 320

∴ [{P(1 + R/100]ⁿ - P} - (PRT/100)] = 320
⇒ [{P(1 + 25/100]³ - P} - {(P × 25 × 3)/100)}] = 320
⇒ P(5/4)³ - P - 3P/4 = 320
⇒ P(125/64) - (P + 3P/4) = 320
⇒ {(125P/64) - (7P/4)} = 320
∴ P = Tk. 1575.38

Given amount = Tk. 1348.32
Principle = Tk. 1200
And time = 2 years

According to the law,
A = P(1 + R/100)ⁿ
1348.32 = 1200(1 + R/100)²
1348.32/1200 = (1 + R/100)²
11236/10000 = (1 + R/100)²
(106/100)² = (1 + R/100)²
(1 + 6/100)² = (1 + R/100)²
R = 6% per annum.

12000 × (1 + R/100)⁵ = 24000
⇒ (1 + R/100)⁵ = 2
⇒ {(1 + R/100)⁵}⁴ = 2⁴ = 16
⇒ (1 + R/100)²⁰ = 16
⇒ P(1 + R/100)²⁰ = P16
⇒ 12000(1 + R/100)²⁰ = 16 × 12000 = Tk. 1,92,000

From the question, you know that R = 6%, T = 4 years, S.I. = Tk.1600

If you apply the above values in the simple interest formula S.I. = PRT/100, you will get
1600 = (P x 4 x 6)/100
⇒ P = (1600 x 100)/6 × 4
⇒ P = 6333.33

Using the above value of P, you have to now calculate C.I. as shown below:
CI = [P(1 + R/100)ⁿ] – P
= [6333.33(1 + 6/100)⁴] - 6333.33
= [6333.33 (106/100)⁴] - 6333.33
= [6333.33× 53/50 × 53/50 × 53/50 × 53/50] - 6333.33
= 7995.68 - 6333.33
= Tk.1662.35

Interest compounded half yearly = 5000(1 + 2/100)²
= 5000(102/100)²
= 5000(1.02)² .........(i)

As we know, A = P(1 + R/100)^t
Interest compound yearly = 5000(1 + 4/100)¹
= 5000(104/100)
= 5000(1.04) ............(ii)

From (i) and (ii)
Required difference = 5000(1.02)² - 5000(1.04)¹
= 5000(1.0404) - 5000(1.04)
= 5202 - 5200
= 2.

The population of the town decreases by 10% every year.
Thus, it has a new population every year. So the population for the next year is calculated on the current year population.
For the decrease, we have the formula A = P(1 - R/100)ⁿ

Therefore,
the population at the end of 5 years
= 10000(1 - 10/100)⁵
= 10000(1 - 0.1)⁵
= 10000 x 0.9⁵
= 5904.9

S.P of Tk. 5000 stock = {(156/100) × 5000}
= Tk. 7800

Income from this stock = tk. {(12/100) × 5000}
= Tk. 600

Let investment in 8 % stock be x and that in 9 % stock = (7800 - x).

Therefore,
x × (8/90) + (7800 - x) × 9/108 = 600 + 70
⇒ 4x/45 + {(7800 - x)/12} = 670
⇒ 16x + 117000 - 15x = 670 × 180
⇒ x = 3600

Money invested in 8% stock at 90 = Tk. 3600
Money invested in 9% at 108 = Tk. (7800 - 3600)
= Tk. 4200.

Face value of each share = Tk.20
Market value of each share = Tk.25
Number of shares = 12500

The amount required to purchase the shares
= 12500 × 25
= 312500

By investing Tk. 1552, income = Tk. 128
By investing Tk. 97, income
= (128/1552) × 97
= Tk 8
∴ Dividend 8%.

Number of shares purchased = 5508/102
= 54.

Income from each share = 4% of Tk. 100
= Tk. 4

∴ Original income = Tk. (54 × 4) = Tk. 216

Money incurred from sale of share = Tk. (105 × 54)
= Tk. 5670

Number of new shares purchased = 5670/126 = 45

New income = Tk. (45 × 5)
= Tk. 225

∴ Change in income = Tk. (225 - 216)
= Tk. 9.

Let investment in 12% stock be Tk. x.
Then,
investment in 15% stock = Tk. (12000 - x)

∴ (12/120) × x + (15/125) × (12000 - x) = 1360
⇒ x/10 + 3/25(12000 - x) = 1360
⇒ 5x + 72000 - 6x = (1360 × 50)
⇒ x = 4000

Hence, Investment in 12% stock is Tk. 4000

Market Value of Company X (his selling price) = Tk. 30
Total shares sold = 4000

The amount he gets = Tk. (4000 × 30)
He invests this amount in ordinary shares of Company Y
Market Value of Company Y(His purchasing price) = Tk. 15

Number of shares of company Y which he purchases = (4000 × 30)/15
= Tk. 8000.

For an income of Tk. 756, investment
= Tk. 9000

For an income of Tk. (21/2), investment
= Tk. {(9000/756) × (21/2)}
= Tk. 125

∴ For a Tk. 100 stock, investment = Tk. 125

The market value of Tk. 100 stock
= Tk. {125 - (1/4)}
= Tk. 124.75

For an income of Tk. 10, investment = Tk. 96
For an income of 12, investment
= Tk. (96/10) × 12
= Tk. 115.20

Hence, He must purchase a stock worth of Tk. 115.20

Number of shares sold = 7500/100
= 75

Proceeds from sale of Tk. 7500 stock
= Tk. [(105.50 - 0.5) × 75]
= Tk. 7875

Number of new shares purchased
= 7875/)124.50 + 0.50
= 7875/125
= 63

Original income
= 10% of Tk. 7500
= Tk. 750

New income
= 14% of Tk. 6300
= Tk. {(14/100) × 6300}
= Tk. 882

∴ Change in income
= Tk. (882 - 750)
= Tk. 132

For an income of Tk. 1 in 9% stock at 96,
investment = Tk. (96/9)
= Tk. 32/3

For an income of Tk. 1 in 12% stock at 120,
investment = Tk. (120/12)
= Tk. 10

Ratio of investments = (32/3) : 10
= 32 : 30
= 16 : 15.

Face Value of a share = Tk. 60
He bought each share at Tk. 60 - Tk. 5 = Tk. 55
Number of shares = 40
Dividend = 12(1/2)%
= (25/2)%

Dividend per share = (60 × 25)/(2 × 100)
= Tk. 7.5

Total dividend = (40 × 7.5)
∴ He got a dividend of (40 × 7.5) for an investment of Tk. (40 × 55)

Interest obtained
= (40 × 7.5 × 100)/(40 × 55)
= 13.64%