Find the rate percent per annum, if Rs. 2000 amount to Rs. 2315.25 in

1.	Find the rate percent per annum, if Rs. 2000 amount to Rs. 2315.25 in an year and a half, interest being compounded six monthly.
Answer» Given, Principal = Rs.2000 Amount = Rs.2315.25 Time \(={1}\frac{1}{2}\) years \(=\frac{3}{2}\) years Let rate = R % per annum A \(={P}[({1}+\frac{R}{100})^T]\) \(={2000}[({1}+\frac{R}{100})^{\frac{3}{2}}]\) = 2315.25 \(=({1}+\frac{R}{100})^{\frac{3}{2}}\) = 1.1576 \(={1}+\frac{R}{100}\) = 1.1025 \(=\frac{R}{100}\) = 0.1025 = R = 10.25% Hence , Rate = 10.25%

Find the rate percent per annum, if Rs. 2000 amount to Rs. 2315.25 in an year and a half, interest being compounded six monthly.

Answer»

Given,

Principal = Rs.2000

Amount = Rs.2315.25

Time \(={1}\frac{1}{2}\) years \(=\frac{3}{2}\) years

Let rate = R % per annum

A \(={P}[({1}+\frac{R}{100})^T]\)

\(={2000}[({1}+\frac{R}{100})^{\frac{3}{2}}]\) = 2315.25

\(=({1}+\frac{R}{100})^{\frac{3}{2}}\) = 1.1576

\(={1}+\frac{R}{100}\) = 1.1025

\(=\frac{R}{100}\) = 0.1025

= R = 10.25%

Hence ,

Rate = 10.25%