Question

If rs 40000 amounts to rs 46305 in 1 1/2 years compound interest payable half yearly find the rate of interest per annum

Answer 1

Hello Dear.

Here is the answer---


Given Conditions ⇒

Amount (A) = Rs. 46,305
Principal(P) = Rs. 30,000

Time(n) = $1 \frac{1}{2}$
   = 3/2 years.
∴ 2n = 2 × 3/2
     = 3 years.

Let the rate of Interest be r.

Now, 
Since the Interest is Payable Half Yearly,

∴ A = P[1 + r/200]²ⁿ
⇒ 46,305 = 40,000[ 1 + r/200]³
⇒ [1 + r/200]³ = 46305/40000
⇒ [1 + r/200]³ = [21/20]³

 On Comparing,
 
 1 + r/200 = 21/20
⇒ r/200 = 21/20 - 1
⇒ r/200 = (21 - 20)/20
⇒ r/200 = 1/20
⇒ r = 10%


∴ Rate of Interest is 10%.


Hope it helps.

Answer 2

Given :-

• Principal = Rs.40000
• Amount = Rs.46305
• Time = (3/2) years.
• Rate = compounded half yearly .

To Find :-

• The rate of interest per annum. ?

Solution :-

we know that, when interest is compounded half yearly ,

• Rate becomes half .
• Time becomes double.

so,

• Time = (3/2) * 2 = 3 years.
• Rate = Let half yearly is R% .

then,

→ P[1 + (R/100)]^T = A

→ 40000[1 + (R/100)]³ = 46305

→ [1 + (R/100)]³ = 46305/40000

→ [1 + (R/100)]³ = 9261/8000

→ [1 + (R/100)]³ = (21/20)³

cube root both sides,

→ 1 + (R/100) = (21/20)

→ (R/100) = (21/20) - 1

→ (R/100) = (21 - 20)/20

→ (R/100) = (1/20)

→ R = 5% .

therefore,

→ The rate of interest per annum = 5 * 2 = 10% (Ans.)

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CI in 2yr is Rs. 1600 and in 3 yrs it will be Rs. 1700. Find the rate of interest.

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