How to Double Check TVM Answers

A lot of students have trouble sorting out if their factor notation representations of cash flows is right. The the trick to double checking your work, and the reason for the last question on the essential question, is to use two different methods.

Take for example the simple cash flow:

Time Asset
0 0
1 0
2 5
3 5

This is just a short, two period long, constant series that needs to be time shifted. You can write the present worth in factor notation as:

(1)
\begin{align} \frac{5 (P|A, i, 2)}{(1+i)^1} \end{align}

You can evaluate that with i = 10% as:

(2)
\begin{align} \frac{5 \frac{(1+.1)^2 -1}{.1 (1+.1)^2 } }{(1+.1)^1}= 7.89 \end{align}

To double check your answer find the present worth via brute force at the same interest rate:

(3)
\begin{align} \frac{5}{(1+.1)^2}+\frac{5}{(1+.1)^3}=7.89 \end{align}

The method is not foolproof. There are a lot of cash flows with the same factor notation but it is a necessary condition for your factor notation representation to be right.

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