Question

You want to have $3000 in your savings account after 3 years. Find the amount you should deposit for each of the situations described below.
a. the account pays 3% annual interest compounded quarterly
b. the account pays 2.25% annual interest compounded monthly
c. the account pays 2% annual interest compounded daily
(SHOW YOUR WORK)

Answer 1

A) take the annual interest and divide it by 4 since it is compounded quarterly.
.03 ÷ 4 = .0075.  Add 1 to include your principal.  1.0075 and raise it to the 12th power since you will be doing this 4 times a year for 3 years (4 x 3 =12).
Since you want 3000 at the end of this period you should do:

3000 ÷ (1.0075¹²) and you get $2742.71  which is how much you should put in.

B) .001875 is the monthly rate of 2.25%  (.0225 divided by 12)
This time we have to do it to the 36th power since there are 36 months in 3 years.
Don't forget to add the 1 to include your money.
3000 ÷ (1.001875¹²) = $2804.36

C) 2% compounded daily means .02 ÷ 365 = (about) .00005479 
Once again we add our principal by putting a 1 in front 1.00005479  
3000 ÷ (1.00005479¹⁰⁹⁵) (1095 because 365 x 3 years = 1095 days)
= $2825.31

Just to emphasize why I always added 1.  Since I am dividing, dividing by 1 givesyou the same as you start with (3000 ÷1 is still 3000)  The small numbers after the 1 reduce the amount (3000) to the amount you will have to put in to realize $3000 at the end of each time period.