# engineering economics: construct the cash flow diagram

A father wants to deposit an unknown lump-sum amount into an investment opportunity 2 years from now that is large enough to withdraw P4000 per year for state university tuition for 5 years starting 3 years from now.

•If the rate of return is estimated to be 15.5% per year, construct the cash flow diagram.

## Draw a horizontal time line…

Draw a horizontal time line from 0 to 8, the numbers in your timeline represents the number of years. At year 2, draw a downward arrow and labeled it $P_2$. We let $P_2$ stands for the lump-sum amount to be deposited by the father 2 years from now. At time-lines 3, 4, 5, 6, and 7, draw upward arrows, and label each with P4000. From the problem, P4000 is the yearly 5-year withdrawal to be made 1 year after the deposit. Solve for $P_2$ using the formula below.

$$P_2 = \dfrac{A[(1 + i)^n - 1]}{(1 + i)^n i}$$

where, $A = 4000$, $n = 5$ and $i = 0.155$

More about annuity: https://mathalino.com/node/1442