ed moura has $10000 invested in stocks paying 9%. how much additional money should he invest in certificates of deposit paying 4% so that the average return on two investments is 5%
.09*10000 + .04x = .05(10000+x)
To determine how much additional money Ed Moura should invest in certificates of deposit (CDs) paying 4% in order to achieve an average return of 5% on his investments, we can use the weighted average formula.
Let x represent the additional amount Ed should invest in CDs. The total amount invested will be $10,000 (in stocks) + x (in CDs).
Now, let's calculate the weighted average:
Average return on two investments = (Amount invested in stocks * Return on stocks) + (Amount invested in CDs * Return on CDs) / Total amount invested
We know that the average return on two investments is 5% and the return on stocks is 9%.
5% = (10,000 * 9%) + (x * 4%) / (10,000 + x)
To solve for x, let's simplify the equation:
0.05 = (0.09 * 10,000) + (0.04 * x) / (10,000 + x)
0.05 = 900 + 0.04x / 10,000 + x
Now, let's cross multiply:
0.05 * (10,000 + x) = 900 + 0.04x
500 + 0.05x = 900 + 0.04x
0.05x - 0.04x = 900 - 500
0.01x = 400
x = 400 / 0.01
x = 40,000
Therefore, Ed Moura should invest an additional $40,000 in certificates of deposit to achieve an average return of 5% on his investments.