Jimmy opens a savings account with a $200 deposit at the beginning of the month. The account earns 4.6% annual interest compounded monthly. At the beginning of each subsequent month, Jimmy deposits an additional $200. How much will the account be worth at the end of 12 years?

Answer 1

The standard formula
amount = paym( (1+i)^n - 1)/i
assumes that payments are made at the end of a payment periods, yours are made at the beginning of each period.
I will pretend we have 145 payments, but then subtract the last one
i = .046/12 = .003833... (I stored in my calculator's memory)
amount = 200( 1.003833...^145 - 1)/.0038333 - 200
= 38,489.12

or , take the present value
PV = 200 + 200(1 - 1.003833..^-143)/.0038333
= 22,185.33
now we have to "move this forward" 144 periods
= 22185.33(1.003833..)^144
= 38,489.13 just like above