Asmall company wishes to set up a fund that can be used for technology purchases over the next 6 years. their forecast is for $18,000 to be needed at the end of year 1, decreasing by $2,000 each year thereafter. the fund earns 9% per year. how much money must be deposited to the fund at the end of year 0 to just deplete the fund after the last withdrawal? $ round entry to the nearest dollar. the tolerance is ±4.

Cash flow diagram:

? k
|
|
|
|
|
|
|
|    1   2  3   4   5   6
|__ __ __ __ __ __ 
     |    |    |    |    |    |
     |    |    |    |    |    |
     |    |    |    |    |    |
     |    |    |    |    |    |
     |    |    |    |    |   8k
     |    |    |    |   10k
     |    |    |   12k
     |    |   14k
     |   16k
   18k

We need the amount x deposited at the end of year 0 (or beginning of year 1) to provide exactly the cash flow shown.
To solve the problem, we can replace the problem by
A. an annual cash-out of A=$18000 for n=6 years, added onto
B. a cash-in gradient of G=$2000 annually starting at the end of year 2.
with a 9% annual rate.

A. Present value of $18000 annual cash-out




B. Present value of G=$2000 annual gradient




Total present value of expenses = -$80746.53+$20184.77=-60561.77
Amount needed at the end of year zero = -(-60561.77)= $60561.77

amount needed to be deposited at the end of year zero is $60561.77 (to the nearest cent).

It’s option c for sure