Finding initial investment

[csmith123]

Question: Cathy wants to have $32,000 in cash 6 years from now in order to pay for improvements that must be made to her small office at that time. If Cathy finds a savings account that pays annual interest of 4.5% compounded monthly, then how much should she invest right now in the account in order to have the funds in 6 years?
Answer: $24,440.48

I know this only because I found an online inital investment calculator. The main problem I'm having is determining the answer because there is only one investment, not multiple investments so the handy dandy TVM Calculator on the TI-83 won't work. (At least not that I can work out.) So what formula am I missing? Thanks!

 

[TchrWill]

Cathy wants to have $32,000 in cash 6 years from now in order to pay for improvements that must be made to her small office at that time. If Cathy finds a savings account that pays annual interest of 4.5% compounded monthly, then how much should she invest right now in the account in order to have the funds in 6 years?
Answer: $24,440.48

I know this only because I found an online inital investment calculator. The main problem I'm having is determining the answer because there is only one investment, not multiple investments so the handy dandy TVM Calculator on the TI-83 won't work. (At least not that I can work out.) So what formula am I missing?

The formula for determining the accumulation of a series of periodic deposits, made at the end of each period, over a given time span, an ordinary annuity, is

.....................S(n) = R[(1 + i)^n - 1]/i

where S(n) = the accumulation over the period of n intervals, R = the periodic deposit, n = the number of interest paying periods, and i = the annual interest % divided by 100 divided by the number of interest paying periods per year.

When an annuity is cumputed on the basis of the payments being made at the beginning of each period, an annuity due, the total accumulation is based on one more period minus the last payment. Thus, the total accumulation becomes

.....................S(n+1) = R[(1 + i)^(n+1) - 1]/i - R

You have S, i and n. Solve for R.