Question

Ed Moura has $97,000 invested in stocks paying 9%. How much additional money should he invest in certificates of deposit paying 5% so that the average return on the two investments is 6%?

Answer 1

Ed Moura should invest an additional $291,000 in certificates of deposit (CDs) at 5% to achieve an average return of 6% on his total investments, calculated through a weighted average equation.

Step-by-step explanation:

To determine how much additional money Ed Moura should invest in certificates of deposit (CD) to achieve an average return of 6%, we can set up a weighted average equation. Ed Moura currently has $97,000 invested in stocks at a 9% return rate. Let's denote the amount of additional money to be invested in CDs at 5% as x. The total investment will then be $97,000 + x, and the total return from both investments should be equal to 6% of the total investment.

The equation can be set up as follows:

0.09(97,000) + 0.05x = 0.06(97,000 + x)

By solving this equation for x:

1. Calculate the return from stocks: 0.09(97,000) = $8,730.
2. Set up the equation: $8,730 + 0.05x = 0.06(97,000 + x).
3. Simplify and solve for x: $8,730 + 0.05x = $5,820 + 0.06x.
4. Subtract 0.05x from both sides: $8,730 = $5,820 + 0.01x.
5. Subtract $5,820 from both sides: $2,910 = 0.01x.
6. Divide both sides by 0.01: x = $291,000.

Ed Moura should invest an additional $291,000 in CDs at 5% to achieve an average return of 6% on his total investments.