Okay, to be honest with you, I don't quite understand your question. For instance, I don't know if that sum is payable when Suzanne hits 18, or if it should be paid monthly until she is 18, or if the way I'm assuming the payment is being done is the right one. Anyway, I wrote it with as much detail as I thought I should include. (I didn't include the first payment in the sum set apart)
But I will assume the latter.
Okay, so we will start where the 1st year starts.
Joe was told that he will have to pay monthly and he set asides his sum S, already paying $525 for the first month.
At the start of month 2, Joe now has S saved, and needs to give $525. The resultant sum saved is therefore S-525.
At the beginning of month 12, after paying, the sum saved will be S-11(525).
Now, at the beginning of month 13, before paying, Joe, will have got 1.06(S-11(525)). And after paying; 1.06(S-11(525)) - 525
Which can be simplified to 1.06S - (1.06)(11)(525) - 525
At the beginning of month 25, after paying, you expect to have:
1.06[1.06S - (1.06)(11)(525) - 12(525)] - 525
\(\displaystyle 1.06^2S - (1.06^2)(11)(525) - (1.06)(12)(525) - 525\)
At month 37;
\(\displaystyle 1.06^3S - (1.06^3)(11)(525) - (1.06^2)(12)(525) - (1.06)(12)(525) - 525\)
At beginning of month 48, after paying;
(Remember the first one we had, it was month 2 and there was one 525. This is month 48, and the total 'number of 525' is 11+12+12+12 = 47)
\(\displaystyle 1.06^3S - (1.06^3)(11)(525) - (1.06^2)(12)(525) - (1.06)(12)(525) - (12)(525)\)
So, that is what I would equate to zero. That would give me: 22,614.98
EDIT: I didn't see your post Subhotosh Khan due to the fact that I started replying before you posted, sorry if my post causes any inconvenience
