Answer:
D. [tex]\frac{x^{2} }{40}[/tex]
Step-by-step explanation:
Compound interest formula is:
[tex]A=p(1+\frac{r}{n})^{nt}[/tex]
When compounded annually;
[tex]A=1000(1+\frac{x}{100})^{1}[/tex]
=> [tex]A=1000(1+\frac{x}{100})[/tex] ....(1)
When compounded semi annually means rate = x/2 and n = 2.
[tex]A=1000(1+\frac{x}{2\times100})^{2}[/tex]
=> [tex]A=1000(1+\frac{x}{200})^{2}[/tex] .... (2)
Now, subtracting 1 from 2 we get ;
[tex]1000(\frac{x^{2} }{40000} )[/tex]
= [tex]\frac{x^{2} }{40}[/tex]
Hence, option D is correct.
