Question

If rs.40000 amounts to 46305 in 3/2 years, compound interest payable half yearly, find the rate of interest per annum?​

Answer 1

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.)