first you need the right formula or a financial calculator.
we'll do the formula and then i'll show you how to do it with an online calculator and then i'll show you how to do it using cash NPV and cash flow through excel.
any one of these will do the job, with various amounts of effort and expertise on our part.
fyi, the manual calculations come from the following tutorial that you might be interested in.
https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f3
so does the reference to the online financial calculators.
normally, the payment is made at the end of each time period, so the formula you need is:
FUTURE VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
f = (a*((1+r)^n-1))/r
f is the future value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods
in your problem, the money is being invested at the end of each quarter and the money is assumed to be compounded each quarter as well.
you are investing at the end of each quarter, so a = 1400
the interest rate if 6% per year compounded quarterly, so r = 6% divided by 4 to get 1.5% per quarter and then divided by 100 to get .015 per quarter.
that's because the formula uses rate and not percent.
she's 25 now and will take the money out of the account when she's 65. unless told otherwise, the underlying assumption is that these are whole years and not partial years.
65 minus 25 = 40 years * 4 quarters per year = 160 quarters, so n = 160.
you have:
a = 1400
r = .015
n = 160
your formula of f = (a*((1+r)^n-1))/r becomes:
f = (1400*((1+.005)^160-1))/.005
solve for f to get f = 917,323.08
that's how much will be in the account when she turns 65.
her total contribution to the account is 160 * 1400 = 224,000.
the total interest that she earned = 917,323.08 minus 224,000 = 693,323.08.
if you used the financial calculator provided in the tutorial, you would do the following.
pv = 0
fv = 0
np = 160
pmt = -1400
ir = 1.5
payment made at the end of each time period.
you would then click on fv and the calculator will tell you that fv = 917,323.08.
this can be seen below.
the following excel printout shows you the remaining balance in each quarter and the payment in each quarter and the interest earned in each quarter for the first few time period and the last few time periods.
the financial calculator used can be found at https://arachnoid.com/finance/index.html
any further questions, give me a shout.
theo