What sum of money amounts to Rs 6000 in 2 years at the rate of 10% per annum?

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A sum of money amounts to Rs. 10240 in 2 years at 6

% per annum, compounded annually. Find the sum.

Let sum = P

Interest rate = 6

Time = 2 years

Now,

Amount (A) = P (1 + R/100)n [Where, P = Present value

R = Annual interest rate

n = Time in years]

∴ A = P[1 + (20/3)/100]2

⇒ 10240 = P [1 + 1/15]2

⇒ 10240 = P [16/15]2

⇒ 10240 = P × 256/225

⇒ P = 10240 × 225/256

⇒ P = 40 × 225

⇒ P = 9000

∴ Sum = Rs.9000

A certain sum of money becomes Rs. 6,000 at certain rate of compound interest in 2 years and Rs. 13,500 in 4 years. Find the sum of money.

1. Rs. 2,666.67
2. Rs. 2,300.67
3. Rs. 2,600
4. Rs. 2,700

Answer (Detailed Solution Below)

Option 1 : Rs. 2,666.67

Given:

A certain sum of money becomes Rs. 6,000 at certain rate of compound interest in 2 years and Rs. 13,500 in 4 years.

Concepts used:

A = P × [1 + (R/100)]T

→ A = Amount, P = Principal, R = Rate of interest, T = Time (in years)

Calculation:

Detailed solution:

A = P × [1 + (R/100)]T 

⇒ Rs. 6,000 = P × [1 + (R/100)]2       ----(1)

A = P × [1 + (R/100)]T 

⇒ Rs. 13,500 = P × [1 + (R/100)]4       ----(2)

Solving equations (1) and (2) by dividing equation (2) by equation (1)

⇒ Rs. 13,500/Rs. 6,000 = P × [1 + (R/100)]4/P × [1 + (R/100)]2  

⇒ 9/4 = [1 + (R/100)]2 

⇒ 3/2 = [1 + (R/100)]

⇒ R/100 = (3/2) - 1

⇒ R = 100/2 %

⇒ R = 50%

A = P × [1 + (R/100)]T 

⇒ Rs. 6,000 = P × [1 + (50/100)]2  

⇒ Rs. 6,000 = P × 9/4

⇒ P = Rs. 6,000 × 4/9

⇒ P = Rs. 2,666.67

∴ The sum of money lent is equal to Rs. 2,666.67.

P = (A1)2/A2 

⇒ Rs. 6,000 × 6,000/Rs. 13,500

⇒ Rs. 2,666.67. 

∴ The sum of money lent is equal to Rs. 2,666.67.

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What sum of money will amount to Rs. 6000 in 5 years at 10% per annum on simple interest?

1. Rs. 5500
2. Rs. 5000
3. Rs. 4000
4. Rs. 4500

Answer (Detailed Solution Below)

Option 3 : Rs. 4000

Free

General Awareness Mock Test

10 Questions 10 Marks 6 Mins

Given:

Amount, A = Rs. 6000

Time, T = 5 years

Rate, R = 10%

Formula used:

Simple Interest = (Principal × Rate × Time)/100

Amount = Principal + Simple Interest

Calculation:

Let the sum of money be Rs. P

Amount = Principal + Simple Interest

⇒ 6000 = (P) + [(P × 10 × 5)/100]      

⇒ 6000 = [P + (P/2)]

⇒ 6000 = 3P/2

⇒ 2000 × 2 = P

⇒ P = 4000

∴ The sum of money is Rs. 4000.

Formula used:

Principal = [(100 × A)/(100 + RT)]

Where,

A = Amount, R = Rate, T = Time

Calculation:

Principal = [(100 × 6000)/(100 + 10 × 5)]

⇒ (6000 × 100)/150

⇒ 40 × 100

⇒ 4000 

∴ The sum of money is Rs. 4000.

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Last updated on Dec 19, 2022

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