Quarterly payment- formula? help!

Quarterly payment necessary to accumulate $350,000 in a fund paying 5.8% per year, compound quarterly, over a period of 25 years if the fund started with an initial deposit, at the beginning of the period, of $2,000.

Since this is a quarterly payment, then we need to
use an ANNUITY formula to calculate the unknown
payment

Now when the payment is
ANNUAL { one per year@ end of each year}, then
the formula is

............................n
....................(1+ i).- 1
Amount = P▬▬▬▬▬
........................i

n= number of periods
i = annual interest rate as decimal
P = Amount of each Payment

If this were annual payments we would use
n=25 i = 0.058


Now for quarterly compounding
we may use this same formula, EXCEPT
n = number of periods.

In this problem it is 25 x 4 = 100

and

i = periodic rate of interest = 0.058/4 = 0.0145

so

............................n
....................(1+ i).- 1
Amount = P▬▬▬▬▬
........................i

becomes

.................................100
....................(1.0145). minus.. 1
350,000 = P▬▬▬▬▬▬▬▬▬
........................0.0145

The formula part to the right of the P is
sometimes called the

Present value annuity factor for nominal
interest rate 0.058 {5.8%}
and quarterly compounding

Solve this for P and that is the needed quarterly payment

Do this work YOURSELF to be sure you know how to get the
needed result. However you may check against my result
and I get

P = $1576.597457
which is always rounded to the
nearest 1 cent at $1576.60

unless you have a teacher, or financial institution
who wants results rounded to te nearest $1.00
and that is $1577

the formula is : F=P(1+(j/m)^tm
wherein F is the maturity value
P is the Principal amount
j is the nominal interest rate
m is the number of conversion per year
t is the time