Ed has $15,000 invested in stocks paying 8%. How much additional money should he invest in certificates of deposit paying 4% so that the average return on the two investments is 6%?
To solve this problem, we need to determine how much additional money Ed should invest in certificates of deposit (CDs) at a 4% interest rate to achieve an average return of 6%.
Let's break down the problem step by step:
1. First, we need to calculate the current annual return on Ed's stock investment. We know that Ed has $15,000 invested in stocks paying 8%, so the annual return on his stock investment can be calculated as follows:
Annual Return on Stocks = ($15,000) * (8%)
= ($15,000) * (0.08)
= $1,200
2. Next, we need to determine the target annual return. Since Ed wants the average return on his investments to be 6%, we can calculate the target annual return as follows:
Target Annual Return = ($15,000 + Additional Investment) * 6%
= ($15,000 + Additional Investment) * 0.06
3. Now, we can set up an equation to solve for the additional amount Ed should invest in CDs. Since the interest rate for CDs is 4%, the annual return on the CDs will be:
Annual Return on CDs = Additional Investment * 4%
= Additional Investment * 0.04
4. We know that the total annual return is the sum of the annual returns from stocks and CDs. So, we can set up the equation:
Annual Return on Stocks + Annual Return on CDs = Target Annual Return
$1,200 + (Additional Investment * 0.04) = ($15,000 + Additional Investment) * 0.06
5. Now, we can solve the equation for the additional investment:
$1,200 + 0.04 * Additional Investment = 0.06 * ($15,000 + Additional Investment)
Simplifying the equation further:
$1,200 + 0.04 * Additional Investment = $900 + 0.06 * Additional Investment
Rearranging the equation:
0.04 * Additional Investment - 0.06 * Additional Investment = $900 - $1,200
Combining like terms:
-0.02 * Additional Investment = -$300
Dividing both sides by -0.02:
Additional Investment = $300 / -0.02
Therefore, the additional amount Ed should invest in CDs is:
Additional Investment = -$300 / -0.02
= $15,000
Thus, Ed should invest an additional $15,000 in certificates of deposit to achieve an average return of 6%.