refer to the cash flow diagram. what is the present worth, p, of the gradient cash flows?\n0 1 2 3 4 5\n$i =…

refer to the cash flow diagram. what is the present worth, p, of the gradient cash flows?\n0 1 2 3 4 5\n$i = 5%$\n$p=?$\na. 600(p/a, 5%, 5) + 100(p/g, 5%, 5)\nb. 600(p/a, 5%, 5) - 100(p/g, 5%, 5)\nc. 200(p/a, 5%, 5) - 100(p/g, 5%, 5)\nd. 200(p/a, 5%, 5) + 100(p/g, 5%, 5)

refer to the cash flow diagram. what is the present worth, p, of the gradient cash flows?\n0 1 2 3 4 5\n$i = 5%$\n$p=?$\na. 600(p/a, 5%, 5) + 100(p/g, 5%, 5)\nb. 600(p/a, 5%, 5) - 100(p/g, 5%, 5)\nc. 200(p/a, 5%, 5) - 100(p/g, 5%, 5)\nd. 200(p/a, 5%, 5) + 100(p/g, 5%, 5)

Answer

Explanation:

Step1: Decompose cash - flows

The cash - flow series can be decomposed into a uniform series and a gradient series. The uniform part has an amount of $A_1 = 200$ and the gradient $G=100$.

Step2: Recall present - worth formulas

The present - worth formula for a uniform series is $P = A(P/A,i,n)$ and for a gradient series is $P = G(P/G,i,n)$.

Step3: Calculate present worth

The present worth of the cash - flow series is the sum of the present worth of the uniform series and the present worth of the gradient series. The present worth of the uniform series with $A = 200$ is $200(P/A,5%,5)$ and the present worth of the gradient series with $G = 100$ is $100(P/G,5%,5)$. So, $P=200(P/A,5%,5)+100(P/G,5%,5)$.

Answer:

D. 200(P/A, 5%, 5) + 100(P/G, 5%, 5)