calculate the corresponding uniform annual withdrawals a2 given that n1 = 14 (see cash flow diagram…

calculate the corresponding uniform annual withdrawals a2 given that n1 = 14 (see cash flow diagram below).\n1 2 3... n1 n1+1 n1+2... n1+5\n$a1 = $2,000\n$i = 6%$\n$a2 =?$\na. 2,000(f/a, 6%, 14)(a/p, 6%, 5)\nb. 2,000(p/a, 6%, 14)(a/f, 6%, 4)\nc. 2,000(p/a, 6%, 13)(a/f, 6%, 4)\nd. 2,000(f/a, 6%, 13)(a/p, 6%, 5)\ne. 2,000(p/a, 6%, 14)(a/f, 6%, 5)

calculate the corresponding uniform annual withdrawals a2 given that n1 = 14 (see cash flow diagram below).\n1 2 3... n1 n1+1 n1+2... n1+5\n$a1 = $2,000\n$i = 6%$\n$a2 =?$\na. 2,000(f/a, 6%, 14)(a/p, 6%, 5)\nb. 2,000(p/a, 6%, 14)(a/f, 6%, 4)\nc. 2,000(p/a, 6%, 13)(a/f, 6%, 4)\nd. 2,000(f/a, 6%, 13)(a/p, 6%, 5)\ne. 2,000(p/a, 6%, 14)(a/f, 6%, 5)

Answer

Explanation:

Step1: First, find the future - value of the first series

The first series of annual payments $A1 = 2000$ occurs for $N1 = 14$ years. The future - value of an ordinary annuity formula is $F=A(F/A,i,n)$. Here, $A = A1=2000$, $i = 6%$, and $n = N1 = 14$. So the future - value of the first annuity at the end of year $N1$ is $F = 2000(F/A,6%,14)$.

Step2: Then, convert the future - value to an equivalent uniform annual series

The future - value obtained in Step 1 is considered as a present - value for the second annuity series that occurs for $n = 5$ years. To convert a present - value $P$ (which is the future - value from Step 1) to an equivalent uniform annual series $A$, we use the capital - recovery factor $(A/P,i,n)$. Here, $i = 6%$ and $n = 5$. So the equivalent uniform annual withdrawal $A2$ is $A2=2000(F/A,6%,14)(A/P,6%,5)$.

Answer:

A. $2,000(F/A,6%,14)(A/P,6%,5)$