ev3001 said:

for the question about the $100 on every birthday, its actually 22 installments, not 21. Becoz its ON her birth + every birthday, so really her first brthday is the second payment, hence 21st brthday is 22nd payment

Yeah. IMO this is a really nasty question.

ev3001 is right. There are 22 payments of $100. So the total amount deposited is certainly 22 x 100 = $2200.

BUT

In this course, Annuities are defined as payments at the END of each year (or month, quarter, etc). The first payment is NOT made at the end of a year. We have to treat that one separtely.

The first payment of $100 is basically compounded at 6% p.a. for 21 years (until the 21st birthday). So this amount on its own grows to 100(1.06)

^{21}.

The other 21 payments form an annuity. The payment on the 1st birthday is the 1st payment of the annuity and so on. So this annuity grows to 100 [ (1.06

^{21} – 1) / 0.06].

So the expression for the total amount is 100(1.06)

^{21} + 100[(1.06

^{21} – 1) / 0.06].