Ed Moura has $29,000 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%?
Ed Moura has
$50000
invested in stocks paying
7%.
How much additional money should he invest in certificates of deposit paying
2%
so that the average return on the two investments is
3%?
To find out how much additional money Ed Moura should invest in certificates of deposit, we can use the concept of weighted averages.
Let's assume that he should invest "x" amount of money in certificates of deposit.
The total investment after investing "x" in certificates of deposit will be $29,000 + "x".
To calculate the average return of the two investments, we need to consider the weighted average of the returns based on the invested amount.
The return from the stocks is 5% of $29,000, which can be calculated as (5/100) * $29,000.
The return from the certificates of deposit is 2% of "x", which can be calculated as (2/100) * "x".
The average return is supposed to be 3% of the total investment, so it can be calculated as (3/100) * ($29,000 + "x").
Now, we can set up the equation:
(5/100) * $29,000 + (2/100) * "x" = (3/100) * ($29,000 + "x")
Multiplying through by 100 to get rid of the decimals:
(5 * $29,000) + (2 * "x") = (3 * ($29,000 + "x"))
Simplifying further:
145,000 + 2x = 87,000 + 3x
Bringing "x" terms to one side and constant terms to the other side:
2x - 3x = 87,000 - 145,000
-x = -58,000
Dividing by -1 to solve for "x":
x = 58,000
Therefore, Ed Moura should invest an additional $58,000 in certificates of deposit to achieve an average return of 3% on his total investment.
To find out how much additional money Ed Moura should invest in certificates of deposit (CDs) at 2%, we need to set up an equation based on the average return of the two investments.
Let's assume the additional amount to be invested in CDs is "x".
The interest earned from Ed's investment in stocks can be calculated using the formula: Interest = Principal × Rate.
So, the interest earned from the stock investment is $29,000 × 0.05 = $1,450.
Similarly, the interest earned from the CDs investment would be (29000 + x) × 0.02 = 0.02x + 0.02(29000) = 0.02x + 580.
Now, to find the average return, we divide the total interest earned by the total investment amount.
Average Return = (Interest from stocks + Interest from CDs) ÷ Total Investment Amount.
Here, the total investment amount is the sum of the initial investment in stocks ($29,000) and the additional amount invested in CDs (x). So, the total investment amount is given by 29,000 + x.
Average Return = (1,450 + 0.02x + 580) / (29,000 + x)
Since the average return should be 3%, we can set up the equation:
3% = (1,450 + 0.02x + 580) / (29,000 + x)
Now, we solve this equation to find the value of "x," which represents the additional amount to be invested in CDs.
return=sum of two returns
.03(29000+Y)=.05(29,000)+.2(Y)
solve for Y.
check my thinking.