Question

The simple interest on a sum of money for 3 years at 5% per annum is 1000. What will be the
compound interest on that sum at the same rate and for the same period?​

Answer 1

Answer:

• Rs 1050.83 will be the compound interest on that sum at the same rate and for the same period.

Step-by-step explanation:

Given that:

• Time period = 3 years
• Rate of Interest = 5% per annum
• Simple interest = Rs 1000

To Find:

• What will be the compound interest on that sum at the same rate and for the same period?

Formula used:

1. S.I. = (P × R × T)/100
2. C.I. = P(1 + R/100)ᵀ - P

Where,

• S.I. = Simple interest
• C.I. = Compound interest
• P = Sum of money/Principal
• R = Rate of Interest
• T = Time period

First we have to find the principal:

⟶ S.I. = (P × R × T)/100

Substituting the values.

⟶ 1000 = (P × 5 × 3)/100

⟶ 1000 = 15P/100

⟶ 15P = (1000 × 100)

⟶ P = 100000/15

∴ Principal = Rs 100000/15 = Rs 6666⅔

Finding the compound interest:

⟶ C.I. = P(1 + R/100)ᵀ - P

Substituting the values.

⟶ C.I. = 6666⅔(1 + 5/100)³ - 6666⅔

⟶ C.I. = 6666⅔(1 + 0.05)³ - 6666⅔

⟶ C.I. = 6666⅔(1.05)³ - 6666⅔

⟶ C.I. = 6666⅔ × 1.157625 - 6666⅔

⟶ C.I. = 7717.5 - 6666⅔

⟶ C.I. = 1050.83 (approx.)

∴ Compound interest = Rs 1050.83

Answer 2

${\bf{Given\::}}$

• The simple interest on a sum of money for 3 years at 5% per annum is 1000.

$\\ {\bf{To\: Find\::}}$

• Compound Interest.

$\\ {\bf{Solution\::}}$

Let,

• Principle (P) is x.

As we know that,

$\orange\bigstar\:{\Large\mid}\:\bf\purple{Simple\: Interest\:=\:\dfrac{P\times{R}\times{T}}{100}\:}\:{\Large\mid}\:\green\bigstar$

Where,

• P = Principle = x

• R = Rate = 5%

• T = Time period = 3 years

• Simple Interest = Rs.1000

$\dashrightarrow\:\tt{1000\:=\:\dfrac{x\times{5}\times{3}}{100}\:}$

$\dashrightarrow\:\tt{1000\:=\:\dfrac{15x}{100}\:}$

$\dashrightarrow\:\tt{15x\:=\:1000\times{100}\:}$

$\dashrightarrow\:\tt{x\:=\:\dfrac{100000}{15}\:}$

$\dashrightarrow\:\bf{x\:=\:6666.67\:}$

Hence,

• Principle is Rs.6666.67.

As we know that,

$\orange\bigstar\:{\Large\mid}\:\bf\blue{Compound\: Interest\:=\:P\:\left(1\:+\:\dfrac{R}{100}\right)^n\:-\:P\:}\:{\Large\mid}\:\green\bigstar$

$:\implies\:\tt{C.I\:=\:6666.67\:\left(1\:+\:\dfrac{5}{100}\right)^3\:-\:6666.67\:}$

$:\implies\:\tt{C.I\:=\:6666.67\:\left(1\:+\:0.05\right)^3\:-\:6666.67\:}$

$:\implies\:\tt{C.I\:=\:6666.67\:\left(1.05\right)^3\:-\:6666.67\:}$

$:\implies\:\tt{C.I\:=\:(6666.67\times{1.157625})\:-\:6666.67\:}$

$:\implies\:\tt{C.I\:=\:6666.67\times{(1.157625\:-\:1)}\:}$

$:\implies\:\tt{C.I\:=\:6666.67\times{0.157625}\:}$

$:\implies\:\bf\pink{C.I\:=\:Rs. 1050.83\:}$

∴ Compound Interest is Rs.1050.83.