Explanation:
Here is how I would work this one out :
Treat the first 4 deposits as an annuity due...calculate the value at the end of the year , then calculate that amount compounded quarterly for 39 more years:
Annuity due: FV = A [ ( (1+i)^n -1) / i ] (1 +i) ] where i = .015/4 = .0125
n = 4 ( one year)
and a = 450
plug in the numbers to find FV = $ 1856.96 at the end of year one.
then use this 'deposit ' compounded quarterly for 39 more years (n = 156)
$ 1856.96 ( 1 + .0125)^156 = $ 12895.17