Question

Find the rate percent per annum, if Rs. $2,000$ amount to Rs. $2,315.25$ in an year and a half, interest being compounded half-yearly.

Answer 1

Amount(A)= $Rs2315.25$

Principal$\left(P\right)$= Rs $2000$

Time=$1.5$yrs

Let rate be '$R^{\prime }$

Since $C.I$ is compounded half yearly

$A=P(1+\frac{R}{2\times 100}{)}^2\times T$

$2315.25=2000(1+\frac{R}{200}{)}^2\times 1.5$

$\frac{2315.25}{100\times 2000}=(1+\frac{R}{100}{)}^3$

$\frac{9261}{100\times 80}=(1+\frac{R}{100}{)}^3$

$(\frac{21}{20}{)}^3=(1+\frac{R}{100}{)}^3$

$\frac{21}{20}=1+\frac{R}{100}$

$R=(\frac{21}{20}-1)\times 100$

$R=\frac{1}{20}\times 100$

$R=5$

Therefore Rate is $5$.