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The compound interest on a sum of money in

2 years and 4 years are Rs 5,460 and Rs 12,066.60
respectively. Find the difference between principal
and compound interest of 3 years.​

User Shauntee
by
4.0k points

1 Answer

9 votes

Answer:

The difference between the principal and the compound interest in three years is Rs 17,994

Explanation:

The compound interest is given according to the following formula;


C.I. = P \cdot \left ( 1 + (r)/(n) \right ) ^(n\cdot t) - P

The given amount of the compound after 2 years = Rs 5,460

The given amount of the compound after 4 years = Rs 12,066.60

Therefore, we have;


5,460 = P \cdot \left ( 1 + (r)/(100) \right ) ^(2) - P...(1)


12,066.60 = P \cdot \left ( 1 + (r)/(100) \right ) ^(4) - P ...(2)

Dividing equation (2) by (1), we have;


(12,066.60)/(5,460) = (P \cdot \left ( \left ( 1 + (r)/(100) \right ) ^(4) - 1\right ))/(P \cdot \left (\left ( 1 + (r)/(100) \right ) ^(2) -1 \right ) ) =(\left ( 1 + (r)/(100) \right ) ^(4) - 1)/(\left ( 1 + (r)/(100) \right ) ^(2) -1 )


Let \ \left ( 1 + (r)/(100) \right ) ^(2) = x, we \ get;


(12,066.60)/(5,460) =(\left ( 1 + (r)/(100) \right ) ^(4) - 1)/(\left ( 1 + (r)/(100) \right ) ^(2) -1 ) = (x^2 - 1)/(x - 1)

∴ 12,066.60 × (x - 1) = 5,460 × (x² - 1) = 5,460 × (x - 1) ×(x + 1)

∴ 12,066.60 × (x - 1)/(x - 1) = 5,460 × (x + 1)

12,066.60/5,460 = x + 1

x = 12,066.60/5,460 - 1 = 1.21 = 121/100

x = 121/100


\left ( 1 + (r)/(100) \right ) ^(2) = x = (121)/(100)


1 + (r)/(100) =\sqrt{ (121)/(100)} = (11)/(10)

We get


(12,066.60)/(5,460) =(221)/(100)


\therefore (12,066.60)/(5,460) =(221)/(100) = \left ( 1 + (r)/(100) \right ) ^(2)


1 + (r)/(100) = \sqrt{ (221)/(100) } = (√(221) )/(10)


(r)/(100) = (√(221) )/(10) - 1


(r)/(100) = (11)/(10) - 1 = (1)/(10) = 0.1

r = 100 × 0.1 = 10%

r = 10%

Therefore, we have;


5,460 = P \cdot \left ( 1 + (r)/(100) \right ) ^(2) - P = P * \left ( 1 + 0.1\right ) ^(2) - P


5,460 = P * \left ( 1 + 0.1\right ) ^(2) - P = P * \left (\left ( 1 + 0.1\right ) ^(2) - 1\right) = P * (21)/(100)


P = (100)/(21) * 5,460 = 26,000

The principal = Rs. 26,000

The compound interest in 3 years is therefore;


CI_3 = 26,000 * \left ( 1 + (10)/(100) \right ) ^(3) - 26,000= 8606

The difference, 'd', between the principal and the compound interest in three years, is given as follows;

d = P - CI₃

d = 26,600 - 8606 = 17994

The difference between the principal and the compound interest in three years, d = Rs 17,994.

User Ramrunner
by
3.5k points