Question

Suppose that you have $6000 to invest. Which investment yields the greater return over 4 years: 8.25% compounded quarterly or 8.3% compounded semiannually?

Answer 1

Of course quarterly investment yields more

Explanation:

Your final Money will be
`M_q=6000*(1+(0.0825/4))^(4*4)`
under compounded quarterly option. Note that there are four quarters in each year and your investment is 4 years.
`M_q=6000*1.3863=$8317.84`

Under semiannual option:
`M_s=6000*(1+0.083/2)^(4*2)`

Note that there are two semiannual periods in one year for a duration of 4 years.

`M_s=6000*1.3844`
`M_s=$8306.64`

Therefore, your quarterly compounding option yields more.