Helen invested $14,000 in an account that pays 3% simple interest. How much additional money must be invested in an account that pays 6% simple interest so that the average return on the two investments amounts to 4% ?
To solve this problem, we need to calculate the additional amount that Helen must invest in an account that pays 6% simple interest.
Let's assume that Helen needs to invest x amount in the account that pays 6% interest.
First, we can calculate the interest earned from the $14,000 investment at 3% interest:
Interest_A = Principal_A * Rate_A = $14,000 * 0.03 = $420
Next, let's calculate the interest earned from the additional investment of x amount at 6% interest:
Interest_B = Principal_B * Rate_B = x * 0.06 = 0.06x
Now, we need to find the average return on the two investments, which should be 4%:
Average Return = (Interest_A + Interest_B) / (Principal_A + Principal_B) = 0.04
Substituting the values we calculated:
0.04 = ($420 + 0.06x) / ($14,000 + x)
To solve for x, we can cross multiply and simplify the equation:
0.04 * ($14,000 + x) = $420 + 0.06x
560 + 0.04x = $420 + 0.06x
0.06x - 0.04x = $560 - $420
0.02x = $140
x = $140 / 0.02
x = $7,000
Therefore, Helen must invest an additional $7,000 in an account that pays 6% simple interest to achieve an average return of 4% on the two investments.
My! You have a major identity problem, John/Brian/Sam/Nancy/Jessica/Mark/Karla!
Please use only one name for your posts.