This problem asks for the future value of an annuity with monthly deposits.
The standard formula for this amount is
FV =R*((1+i)^{n}1)/i,
where R is the payment per compounding period, i = the interest rate per compounding period, and n the number of compounding periods. This formula assumes that one payment is made each compounding period, which in your problem is not the case: the compounding
period is a month (n=30*12), while a payment R=10,000 is made once year.
We can get an approximation if we assume instead that a payment of R=$10,000/12 is made every month.
With i=0.06/12 we get
FV =(10000/12) *((1+(0.06/12))^{30*12}1)/(0.06/12)
=$ 837,100
This is an overestimate, because it assumes monthly payments with monthly compounding.
We can get an underestimate if we assume annual compounding with annual payments. In this case n=30, i=0.06 and
FV=10000 * ((1+0.06)^{30}1)/0.06
=$ 790,580
The actual answer will lie between these two estimates.
Sep 15

Andre W.