$23,394 is approximately right but, depending how close you look at the problem, maybe not quite right.
It comes from =FV(rate, nperiods, pmt, pv, type)
It comes from =FV( (1.55%/4), (20*4), 250, 0, 0)
This is a tricky problem. Here's why the above is not exact:
- Cryptic is compounding the amount quarterly, (at 1/4 the rate), not annually
- Cryptic is using an "end of period" payment. My read of the question is, use a "start of period" payment.
So here's how I would do it, it would require 2 steps.
First, how much is it worth if Gabby saves $250 a quarter for 1 year, with interest paid at the end of the year? (savings put at the start of the year).
You do this in the spreadsheet, 250 every quarter, work out the quarter's interest (at 1.55% / 4), but don't credit the interest until the end of the year. interest is $9.6875. You try.
Second, we can now use the =FV() formula, with 20 periods (which is correct, not 80 periods), because the interest is compounded _annually_ not quarterly.
my answer: = FV(annu_rate, nperiods, annual_pmt, pv, type)
my answer: = FV(1.55%, 20, $1009.6875, 0, 0) = $23,462.97
why have I put 0 (end of period) in the type? because I used the future value of 4 quarterly payments of $250, i.e. how much they are worth at the _end_ of the year, not their PV.
You should get the same result if you do a table of 80 payments in a list in excel (remember to credit the interest at the end of 4 periods, not each row).
That's just my opinion, but maybe I over-analysed the question.