Find the future worth of the cash flow diagram below

Economics Dec 11, 2020

Find the future worth of the cash flow diagram below. Assume i=10% per year. F10 = ? 1 2 3 4 5 6 7 8 9. 10 $400 $500 $600 $700 $800 i = 10%/year $900

Expert Solution

Now, the cash flows at each time is given in the diagram. There are cash flows of $900 at time 0,1,2,3,4. There are cash flows of $800 at time 5, $700 at time 6, $600 at time 7, $500 at time 8, and $400 at time 9. We need to calculate future worth at time 10, with the interest rate of 10% per year. Note that the Future Value factor for any cash flow at time t to time 10 is given by:

FV factor = (1 + i)^10-t

Hence, the future worth of the given cash flows at time 10 is:

$900 × 1.10¹⁰ + $900 × 1.10⁹ + $900 × 1.10⁸ + $900 × 1.10⁷ + $900 × 1.10⁶ + $800 × 1.10⁵ + $700 × 1.10⁴ + $600 × 1.10³ + $500 × 1.10² + $400 × 1.10 = $13890.88

Hence, the future worth is $13890.88

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