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

D.
`(x^(2) )/(40)`

Explanation:

Compound interest formula is:

`A=p(1+(r)/(n))^(nt)`

When compounded annually;

`A=1000(1+(x)/(100))^(1)`

=>
`A=1000(1+(x)/(100))` ....(1)

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

`A=1000(1+(x)/(2*100))^(2)`

=>
`A=1000(1+(x)/(200))^(2)` .... (2)

Now, subtracting 1 from 2 we get ;

`1000((x^(2) )/(40000) )`

=
`(x^(2) )/(40)`

Hence, option D is correct.