Question

if 40000 amounts to 46305 at the rate of 4% per annum compounded annually calculate the time​

Answer 1

Given Conditions ⇒  

Amount (A) = Rs. 46,305

Principal(P) = Rs. 30,000

Time(n)   = 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%.