Ed Moura has $91000 invested in stocks paying 5%. How much additional money should he invest in certificates of deposit paying 2% so that the average return on the two investments is 3%?
.05 * 91000 + .02x = .03(91000+x)
To solve this problem, we need to use the concept of weighted averages.
Let's assume that Ed Moura invests an additional amount, x, in certificates of deposit (CD) at 2% interest.
The total investment would then be $91000 + x.
Now, let's calculate the weighted average return using the formula:
(weight of the first investment * return of the first investment) + (weight of the second investment * return of the second investment) = average return
In this case, the first investment is $91000 in stocks at 5% return and the second investment is x in CDs at 2% return. The average return we are aiming for is 3%.
So, we can write the equation as:
(91000 * 0.05) + (x * 0.02) = (91000 + x) * 0.03
Now, let's solve this equation for x:
4550 + 0.02x = 2730 + 0.03x
0.02x - 0.03x = 2730 - 4550
-0.01x = -1820
Dividing both sides by -0.01:
x = -1820 / -0.01
x = 182000
Therefore, Ed Moura should invest an additional $182000 in certificates of deposit to achieve an average return of 3% on his investments.