help needed for finance.

[Khb_taylors]

Ottawa Manor would like to buy some additional land and build a new assisted living center. The
anticipated total cost is $12.4 million. The CEO of the firm is quite conservative and will only do this
when the company has sufficient funds to pay cash for the entire construction project. Management has
decided to save $235,000 a month for this purpose. The firm earns 7 percent compounded monthly on
the funds it saves. How long does the company have to wait before expanding its operations?

 

[tkhunny]

This is a simple accumulaton. What have you tried?

i = 0.07
i12 = i/12 = 0.0058333...
r = 1+i12
n is the number of required payments

\(\displaystyle 235,000(r + r^{2} + r^{3} + ... + r^{n}) = 235000\left(\frac{r - r^{n+1}}{1-r}\right)\)

I get n = 45.902.

I'll let you ponder the significance of a non-integer value.