Future Value with Multiple Cash Flows You plan to make a series of deposits in an individual retirement account. You will deposit $1,000 today, $2,000 in two years, and $2,000 in five years.

Question

Future Value with Multiple Cash Flows You plan to make a series of deposits in an individual retirement account. You will deposit $1,000 today, $2,000 in two years, and $2,000 in five years. If you withdraw $1,500 in three years and $1,000 in seven years, assuming no withdrawal penalties, how much will you have after eight years if the interest rate is 7 percent? What is the present value of these cash flows?

Accepted Answer

We will calculate the future values for each of the cash flows separately and then add them up. Notice that we treat the withdrawals as negative cash flows:

$[latex]1,000×1.07^{8}[/latex]=$1,000×1.7182=$1,718.19

$[latex]2,000×1.07^{6}[/latex]=$2,000×1.5007 =3,001.46

–$[latex]1,500×1.07^{5}[/latex]=–$1,500×1.4026=– 2,103.83

$[latex]2,000×1.07^{3}[/latex]=$2,000×1.2250=2,450.09

–$[latex]1,000×1.07^{1}[/latex]=–$1,000×1.0700=[latex]\underline{– 1,070.00}[/latex]

Total future value=$[latex]\underline{\underline{3,995.91}}[/latex]

This value includes a small rounding error.
To calculate the present value, we could discount each cash flow back to the present or we could discount back a single year at a time. However, because we already know that the future value in eight years is $3,995.91, the easy way to get the PV is just to discount this amount back eight years:

Present value=$[latex]3,995.91/1.07^{8}[/latex]

=$3,995.91/1.7182

=$2,325.64

We again ignore a small rounding error. For practice, you can verify that this is what you get if you discount each cash flow back separately.

Question 6.S-T.2: Future Value with Multiple Cash Flows You plan to make a ser...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions