Answer:
20%
Step-by-step explanation:
To find the interest rate per annum, we can use the Compound Interest formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\\\\A=P\left(1+\dfrac{r}{n}\right)^{nt}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\\\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the annual interest rate (in decimal form).}\\\phantom{ww}\bullet\;\;\textsf{$n$ is the number of times interest is applied per year.}\\\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}[/tex]
The final account balance (A) is the sum of the interest accrued (Rs 26,480) and the principal invested (Rs 80,000).
Therefore, in this case:
- A = Rs 26,480 + Rs 80,000 = Rs 106,480
- P = Rs 80,000
- n = 2 (semi-annually)
- t = 1.5 years
Substitute the values into the formula and solve for r:
[tex]106480=80000\left(1+\dfrac{r}{2}\right)^{2 \cdot 1.5}\\\\\\\dfrac{106480}{80000}=\left(1+\dfrac{r}{2}\right)^{3}\\\\\\1.331=\left(1+\dfrac{r}{2}\right)^{3}\\\\\\\sqrt[3]{1.331}=1+\dfrac{r}{2}\\\\\\1.1=1+\dfrac{r}{2}\\\\\\\dfrac{r}{2}=1.1-1\\\\\\\dfrac{r}{2}=0.1\\\\\\r=0.1 \cdot 2\\\\\\r=0.2\\\\\\r=20\%[/tex]
Therefore, the interest rate per annum is:
[tex]\LARGE\boxed{\boxed{\sf 20\%}}[/tex]
