Question

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. 5x
B. 10x
C. x^2/20x220
D. x^2/40
E. (10x+x^2/40)

Answer 1

Answer:

D. $\frac{x^{2} }{40}$

Step-by-step explanation:

Compound interest formula is:

$A=p(1+\frac{r}{n})^{nt}$

When compounded annually;

$A=1000(1+\frac{x}{100})^{1}$

=> $A=1000(1+\frac{x}{100})$   ....(1)

When compounded semi annually means rate = x/2 and n = 2.

$A=1000(1+\frac{x}{2\times100})^{2}$

=> $A=1000(1+\frac{x}{200})^{2}$   .... (2)

Now, subtracting 1 from 2 we get ;

$1000(\frac{x^{2} }{40000} )$

= $\frac{x^{2} }{40}$

Hence, option D is correct.