Common Patterns Question 1

Question:

Pop Quiz: Oct 17th
f_lineargradim_5d04d2b.png

Using the linear gradient above, find the present worth and future worth with a 0% interest rate.

Answer:

(1)
\begin{equation} Present worth = 15 \end{equation}
(2)
\begin{equation} Future Worth = 15 \end{equation}

With a 0% interest rate we simply add the values from all periods together, yielding 15. Or, we could conduct PW and FW calculations using the brute force method, both yielding 15.

(3)
\begin{equation} Present Worth = 0/1 + 1/1^2 + 2/1^3 + 3/1^4 + 4/1^5 + 5/1^6 = 15 \end{equation}
(4)
\begin{equation} Future Worth = 0(1)^6 + 1(1)^5 + 2(1)^4 + 3(1)^3 + 4(1)^2 + 5(1) = 15 \end{equation}

If you try to use the linear gradient equation to calculate the present worth or the future worth you will note that you can't evaluate the function. The derivation assumes that the interest rate is not zero.

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