robin invests $50 on the first of every month into a superannuation account.

Question

His employer, Batman, pays 9% of Robin's monthly income of $2500 at the
end of the month into the same account. Interest is paid at the rate of 6% p.a.
compounded monthly.
(a) Calculate the total amount in the account after 45 years.
(b) How much more should Robin invest each month if he wishes to have a
superannuation fund value of $1 000 000 after 45 years?

Answer 1

Since the common formula for the amount of an annuity :
amount = Payment( (1+i)^n - 1)/i
is base on the fact that the payment is made at the end of the period, the only twist that I see in the question would be the first month and the last month.
I will also assume that the end of one month is equivalent to the beginning of the next months

Beginning of month 1 --- 50
Beginning of month 2 --- 50+225
Beginning of month 3 --- 50+225
.....
Beginning of month 539 --- 50+225
Beginning of month 540 --- 50+225
End of month 540--------- 225

I see it as
50(1.005^540 - 1)/.005 (1.005) + 225(1.005^540 - 1)/.005
= ...

let me know what you get.