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].