Question

A sum of USD 4420 should be divided between John and Bob in such a way that after 5 and 7 years, the amount they get is equal, respectively. If the rate of interest is 10 percent, then what is the share of John and Bob?

Answer 1

Answer:

Step-by-step explanation:

Given A sum of USD 4420 should be divided between John and Bob in such a way that after 5 and 7 years, the amount they get is equal, respectively. If the rate of interest is 10 percent, then what is the share of John and Bob?

Let John's share be J and Bob's share be 4420 - J

According to question John = Bob

  J(1 + 10/100)^5 = (4420 - J)(1 + 10/100)

 J(11/10)^5 = (4420 - x)(1 + 10/100)^7

161051 x = (4420 - J)(19487171/10000000)

 J = 2420

So 4420 - 2420 = 2000

So share of John = 2420 and Bob will be 2000

Answer 2

Answer:

Step-by-step explanation:

Question has not specified the rate of interest as Simple or Compounding?

So Here are the solution for both cases.

Case 1 : Assuming Simple interest  

Total Sum = $ 4420

Let say John Share = $ X

Then Bob Share = $ (4420 – X)

Rate of interest = 10 % per annum  

Simple interest = P * R * T / 100

P = Principle (Amount Invested), R = Rate of Interest Per annum, T = Time period in Years

John will earn interest in 5 years =  (X * 10 * 5 )/100 =  $ X/2

John Total amount after 5 Years = X + X/2 = 3X/2 =  $ 1.5X

Bob will earn interest in 7 Years = ((4420-X) * 10 * 7)/ 100 = $ (3094 – 0.7X )

Bob Total Amount after 7 Years = (4420 – X) + (3094 – 0.7X ) = $ (7514 – 1.7X )

Both Amounts would be equal

 1.5X = 7514 – 1.7X

 3.2X = 7514

 X = 2348.125

John Share = $ 2348.125

Bob Share =  $ 4420 - $ 2348.125 = $ 2071.875

Bob Share = $ 2071.875

Case 2 : Considering Compound Interest

Total Sum = $ 4420

Let say John Share = $ X

Then Bob Share = $ (4420 – X)

Rate of interest = 10 % per annum  

Amount including Compound interest = P (1 + R/100)T

P = Principle (Amount Invested), R = Rate of Interest Per annum, T = Time period in Years

John Total amount after 5 Year = X * ( 1 + 10/100)^5  = X * (1.1)5  

Bob Total Amount after 7 Years = (4420 – X) *( 1 + 10/100)7 = (4420-X)*(1.1)7

Both Amounts would be equal

 X * (1.1)5 = (4420-X)*(1.1)7

Cancelling (1.1)5 from both sides

 X = (4420-X)*(1.1)2

 X = (4420 –X) * 1.21

 X = 5348.2 – 1.21X

 2.21X = 5348.2

 X = 5348.2/2.21

 X = 2420

John Share = $ 2420

Bob Share = $ 4420 – $ 2420 = $ 2000

Bob Share = $ 2000