Simple and Compound Interest, Stock

Question: A sum of money doubles itself in 4 years at a certain rate of simple interest. In how many years will it become four times itself at the same rate of interest?

Solution:
মনে করি, আসল (P) = 100 টাকা
4 বছরে এটি দ্বিগুণ হয়ে হয় (A) = 200 টাকা
∴ 4 বছরের সুদ (I) = 200 - 100 = 100 টাকা

অর্থাৎ, 100 টাকা সুদ হতে সময় লাগে 4 বছর।

এখন, আসল চারগুণ হলে সবৃদ্ধিমূল (A) হবে = 400 টাকা
∴ তখন প্রয়োজনীয় মোট সুদ (I) = 400 - 100 = 300 টাকা

এখন,
100 টাকা সুদ হতে সময় লাগে 4 বছর
1 টাকা সুদ হতে সময় লাগে 4/100 বছর
300 টাকা সুদ হতে সময় লাগে (4 × 300)/100 বছর
= 12 বছর

∴ আসল বা মূলধন 12 বছরে চারগুণ হবে।

Question: To produce an annual income of TK 800 from a 8% stock at 80, the amount of stock needed is-

Solution:
since face value is not given, take it as TK 100
As it is a 8% stock, income(dividend) per stock = TK 8
ie, For an income of TK 8, the amount of stock needed = TK 100
For an income of TK 800, the amount of stock needed = (100 × 800)/8 = 10,000

Question: The difference (in taka) between simple and compound interest at 4% per annum on a sum of Tk 1500 after 2 years is:

Solution:
Simple interest, I = Pnr/100 
= (1500 × 2 × 4)/100
= 120 Tk

Compound interest, A = P{1 + (r/100)}²
= 1500{1 + (4/100)}²
= 1500{1 + (1/25)}²
= 1500 × (26/25)²  
= 1622.4 Tk

Interest = 1622.4 - 1500 = 122.4 Tk
 ∴ Difference = 122.4 - 120 = 2.4 Tk

Number of shares = 20000
Face value of each share = Tk. 10
dividend per share = (10 × R/100) where R is the Rate of interest.
Total dividend = 20000 ×10 ×R/100
20000 ×10 ×R/100 = 24000
R = 24000/2000
= 12
Hence the dividend is 12%.

Question: A farmer borrowed Tk. 3600 at 15% simple interest per annum. At the end of 4 years, he cleared this account by paying Tk. 4000 and a cow. The cost of the cow is:

Solution:
P = 3600 tk, R = 15%, T = 4 yrs

S.I = PRT/100
= (3600 × 15 × 4)/100
= 2160 Tk.

Hence,
amount after 4 years = (3600 + 2160) = 5760 Tk.
∴ Cost of the cow = (5760 – 4000) = 1760 Tk.

Face value of each share = Tk. 5
Total dividend received by Jobayed = {100 × 5 × (12/100)}
= Tk. 60
Let market value of 100 shares = Tk. x
x × (10/100) = 60
x = 600
ie, Market value of 100 shares = Tk. 600
Hence, Market value of each share = Tk. 6

Question: A man deposits Tk. 600 in a bank at 10% interest rate compounded annually. At the end of the second year, what will be the total amount including interest?

Solution:
Given,
Principal, P = 600 Tk
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 2 years

We know,
Compound Amount = P(1 + r)ⁿ
= 600 × (1 + 1/10)²
= 600 × (11/10)²
= 600 × (11/10) × (11/10)
= 600 × 121/100
= 726 Tk

Question: What will be the simple interest on Tk. 730 at 9% per annum for the period from January 12, 2026 to May 31, 2026?

Solution: 
January 12, 2026 to May 31, 2026 = 140 days

100 টাকার 365 দিনের মুনাফা = 9 টাকা 
1 টাকার 1 দিনের মুনাফা = 9/(365 × 100) টাকা 
730 টাকার 140  দিনের মুনাফা = (9 × 730 × 140)/(365 × 100) টাকা 
= 25.20

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%.

Let the loan amount be Tk. x
Then,
⇒ (6x/100)+(7.5x/100)+(9x/100) = 8190
⇒ 22.5x = 819000
⇒ x = 36400

Given, Principal, P  = 2800
Compound rate, R  =  10% per annum  =  10/2  =  5% half - yearly
Amount  =  [2800 × (1  +  10/100) × (1  +  5/100)] 
=  (2800 × 11/10 × 21/20)
=  3234
∴ C.I. = (3234 − 2800)  =  434

Question: A sum of money triples itself in 25 years at simple interest. What is the annual interest rate?

Solution:
ধরি, আসল = P টাকা
∴ 25 বছরে সুদে-আসলে হয় (A) = 3P টাকা
সুতরাং, সুদ (I) = A - P = 3P - P = 2P টাকা
সময় (n) = 25 বছর
সুদের হার (r) = ?

আমরা জানি,
I = (Pnr)/100
⇒ r = (I × 100)/(P × n)
⇒ r = (2P × 100)/(P × 25)
⇒ r = (2 × 100)/25
⇒ r = 2 × 4
⇒ r = 8%
সুতরাং, বার্ষিক সুদের হার 8%।

Question: Tk. 10000 becomes Tk. 12000 in 4 years at a certain rate of simple interest. If the rate becomes 2.5 times of itself, the amount of same principal in 6 years will be -

সমাধান:
10000 টাকা 4 বছরে 12000 টাকা হয়।
∴ 4 বছরে সুদ = 12000 - 10000 টাকা = 2000 টাকা
1 বছরে সুদ = 2000/4 = 500 টাকা

2.5 গুণ বৃদ্ধিতে নতুন 1 বছরের সুদ = 500 × 2.5 টাকা
= 1250 টাকা

6 বছরে মোট সুদ = 1250 × 6 টাকা = 7500 টাকা
সুতরাং, 6 বছর পর সুদাসলে হবে = 10000 + 7500 টাকা
= 17500 টাকা

10% সুদে, 1,000 টাকার 4 বছরের সুদ = (10 × 4 × 1000)/100
= 400 টাকা ।
আমরা জানি,
Compound amount, c = p(1 + r)ⁿ
= 1000{1 + (10/100)}⁴
= 1000(11/10)⁴
= 1464.10 টাকা
∴ Compound interest = 1464.10 - 1000
= 464.10 টাকা
∴ Simple এবং Compound interest এর মধ্যে পার্থক্য = 464.10 - 400
= 64.10 টাকা
Answer: 64.10

Question: A town experiences a 10% decrease in its population every year. If the population was 20,000 two years ago, what is the population now?
(এক শহরের জনসংখ্যা প্রতি বছরে ১০% কমে যায়। যদি দুই বছর আগে জনসংখ্যা ২০,০০০ ছিল, তাহলে বর্তমানে জনসংখ্যা কত হবে?)

Solution:
বর্তমান জনসংখ্যা = 20000(1 - 10/100)² {[C = p(1 - r)ⁿ] অনুসারে।}
= 20000 × 0.9 × 0.9
= 16,200

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: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk. 12000 after 3 years at the same rate?

Solution:
Given that,
Increase in amount after 6 years = 60%

We know,
A = P(1 + r/100)n
simple Interest = (principal × rate × time)/100

Now,
Let the amount at the 1^st year be 100x
∴ Increased in amount = 60% of 100x = 60x
⇒ 60x = (100x × 6 × r)/100
⇒ 6r = 60
⇒ r = 60/6 = 10
∴ r = 10% 

∴ Compound Interest after 3 years = P(1 + r/100)ⁿ - P
= 12000(1 + 10/100)³ - 12000
= 12000 × (11/10)³ - 12000
= 12000 × (11/10) × (11/10) × (11/10) - 12000
= 15972 - 12000
= Tk. 3972

∴ The required answer is Tk. 3972

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.

Amount = Tk.(30000+4347) = Tk.34347
let the time be n year
Then,
30000(1+7/100)n = 34347
(107/100)n = 34347/30000 = 11449/10000 = (107/100)2
n = 2year

Question: A person took a loan of Tk. 2500 with simple interest for as many years as the rate of interest. If they paid Tk. 1600 as interest at the end of the loan period, what was the rate of interest?

Solution:
ধরি, সুদের হার = r%
যেহেতু সময় এবং সুদের হার সমান,
∴ সময়, n = r বছর
আসল (P) = 2500 টাকা
মোট সুদ (I) = 1600 টাকা
আমরা জানি,
সরল সুদ, SI = (P × r × n)/100
⇒ 1600 = (2500 × r × r)/100 [এখানে, n = r]
⇒ 1600 = 25 × r²
⇒ r² = 1600/25
⇒ r² = 64
⇒ r = √64
⇒ r = 8

∴ সুদের হার ছিল 8%।

Question: What is the total interest on Tk. 1,200 at 10% per annum for 9 months?

Solution: 
Given,
Principal (P) = Tk. 1200
Rate (R) = 10%
Time (T) = 9 months
= 9/12 year
= 3/4 year

By Formula,
SI = PRT/100
= {1200 × 10 × (3/4)}/100
= (1200 × 10 × 3)/400
= 90 Tk

C.I. when interest compound yearly = Tk. [5000 × (1 + 4/100) (1 + 1/2 × 4/100)]
= Tk. 5304.
C.I. when interest is compounded half-yearly = Tk. 5000 (1 + 2/100)³
= Tk. 5306.04
Difference = Tk. (5306.04 - 5304)
= Tk. 2.04