Question

if the simple intrest and compound interest of of certian sum of money for two years are RS. 8400 and RS. 8652 then find the sum of money the rate of the simple intrest​

Answer 1

Given that:

• The simple interest and compound interest of certain sum of money for two years are Rs. 8400 and Rs. 8652.

To Find:

1. The sum of money.
2. The rate of the interest.

We know that:

In simple interest.

• S.I. = (P × R × T)/100

In compound interest.

• C.I. = P(1 + R/100)ᵀ - P

Where,

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

We have:

• Simple interest = Rs 8400
• Compound interest = Rs 8652
• Time = 2 years

Let us assume:

• The certain sum of money be P.
• The rate of the interest be R.

According to the question.

↣ S.I. = 8400

↣ (P × R × 2)/100 = 8400

↣ 2PR/100 = 8400

↣ PR/50 = 8400

↣ PR = 8400 × 50

↣ PR = 420000 (i)

↣ C.I. = 8652

↣ P(1 + R/100)² - P = 8652

↣ P(1 + 0.01R)² - P = 8652

Using (a + b)².

↣ P{(1)² + (0.01R)² + 2(1 × 0.01R)} - P = 8652

↣ P{ 1 + 0.0001R² + 0.02R} - P = 8652

↣ P + 0.0001PR² + 0.02PR - P = 8652

Cancelling P.

↣ 0.0001(PR)R + 0.02(PR) = 8652

Substituting the value of PR from eqⁿ (i).

↣ 0.0001(420000)R + 0.02(420000) = 8652

↣ 42R + 8400 = 8652

↣ 42R = 8652 - 8400

↣ 42R = 252

↣ R = 252/42

↣ R = 6

∴ Rate of interest = R = 6% per annum

In equation (i).

↣ PR = 420000

Putting the value of R.

↣ P(6) = 420000

↣ 6P = 420000

↣ P = 420000/6

↣ P = 70000

∴ Sum of money = Rs 70000

Hence,

1. The sum of money is Rs 70000.
2. The rate of the interest is 6% per annum.

Answer 2

Given :-

If  the simple intrest and compound interest of of certian sum of money for two years are RS. 8400 and RS. 8652

To Find :-

Sum of money

Rate

Solution :-

Let the principal be p

And rate be r

SI = PRT/100

SI = p × r × 2/100

SI = 2pr/100(1)

Now

CI = P{(1 + r/100)ⁿ - 1}

CI = p{(1 + r/100)² - 1}

CI = p{1 + 2r/100 + r²/(100)² - 1}

CI = p{1 - 1 + 2r/100 + r²/100²}

CI = p{2r/100 + r²/100²}

Taking 100 and r as common

CI = pr/100(2 + r/100) (2)

Now We may divide both equations

{pr/100(2 + r/100)}/{2pr/100} = 8652/8400

{2 + r/100}/{2/100} = 4326/4200

{2 + r/100} = 4326/4200 × 2

r/100 = 4326/2100 - 2

r/100 = 4326 - 4200/2100

r/100 = 126/2100

r = 126/2100 × 100

r = 12600/2100

r = 6%

Now

Using 1

8400 = p × r × 2/100

8400 = p × 6 × 2/100

8400 = p × 12/100

8400 = p × 3/25

8400 × 25/3 = p

2800 × 25 = p

70000 = p