How much more interest will maria receive if she invests 1000$ for one year at x % annual interest, compounded semianually, than if she invest 1000$ for one year at x percent annual interest, compounded annually?A. 5xB. 10xC. x^2/20x220D. x^2/40E. (10x+x^2/40)
Accepted Solution
A:
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.