Question

"A small company wishes to set up a fund" that can be used for technology purchases over the next 6 years. Their forecast is for $12,000 to be needed at the end of year 1, decreasing by $2,000 each year thereafter. The fund earns 8% per year. How much money must be deposited to the fund now to just deplete the fund after the last withdrawal?

Answer 1

$34,438.11

Step-by-step explanation:

The explanation is given in the picture below

Answer 2

The money that must be deposited to the fund now to just deplete the fund after the last withdrawal is $34,428.

Step-by-step explanation:

This is a case of decreasing annuity, in which every year is decreased a fixed ammount. In this case, the decrease does not have a constant rate, so the formula for a increasing (or decreasing) annuity is not applicable.

We have to calculate the present value in a traditional way:

`PV=\sum_(k=1)^6CF_i/(1+i)^k\\\\PV=12,000/(1.08)+10,000/(1.08)^2+8,000/(1,08)^3+6,000/(1.08)^4+4,000/(1.08)^5+2,000/(1.08)^6\\\\PV= 11,111+ 8,573 +6,351+ 4,410+ 2,722+1,260\\\\PV=34,428`