Aimee inherited $15,000. She chose to invest it in a series of municipal bonds, mutual funds, and money market accounts, which paid annual interest rates of 5%, 6%, and 4%, respectively. She invested $2,000 more in mutual funds than she invested in bonds. After the first year, she received a total of $730 in simple interest. How much did she invest in each category?
Let the amounts be x,y,z. Then the facts are:
x+y+z = 15000
y = x+2000
.05x + .06y + .04z = 730
Now just solve for x,y,z
5
56
7
Well, well, well, let's solve this financial riddle, shall we?
Let's start by assigning some variables. Let's say Aimee invested X dollars in bonds. That means she invested X + 2,000 dollars in mutual funds. And she invested X dollars in money market accounts.
Now, let's calculate the amount of interest she earned from each investment. She earned 5% interest on her bonds, which is 0.05X. She earned 6% interest on her mutual funds, which is 0.06(X + 2,000). And she earned 4% interest on her money market accounts, which is 0.04X.
The total interest she earned from all three investments is $730. So, let's set up an equation:
0.05X + 0.06(X + 2,000) + 0.04X = 730
Now, let's solve this equation and find the value of X.
0.05X + 0.06X + 120 + 0.04X = 730
0.15X + 120 = 730
0.15X = 610
X = 610 / 0.15
X = 4,066.67
Okay, now we know that Aimee invested $4,066.67 in bonds. She also invested $4,066.67 + $2,000 = $6,066.67 in mutual funds. And she invested $4,066.67 in money market accounts.
Phew! Aimee is quite the investor, isn't she? I hope she made some wise choices with her money!
To solve this problem, we will use a system of equations. Let's break down the given information into mathematical equations:
Let x be the amount invested in municipal bonds.
Since Aimee invested $2,000 more in mutual funds than in bonds, the amount invested in mutual funds will be: x + $2,000.
The remaining amount (inheritance - amount invested in bonds and mutual funds) will be invested in money market accounts, which is equal to: $15,000 - (x + (x + $2,000)) = $15,000 - (2x + $2,000) = $15,000 - 2x - $2,000.
Now let's calculate the interest earned from each investment:
Interest from municipal bonds = x * 5% = 0.05x.
Interest from mutual funds = (x + $2,000) * 6% = 0.06(x + $2,000) = 0.06x + $120.
Interest from money market accounts = ($15,000 - 2x - $2,000) * 4% = 0.04($15,000 - 2x - $2,000) = 0.04($15,000 - 2x - $2,000) = 0.04($13,000 - 2x).
We are given that the total interest received after the first year is $730, so we can set up the equation:
0.05x + 0.06x + $120 + 0.04($13,000 - 2x) = $730.
Now, let's solve for x:
0.05x + 0.06x + $120 + 0.04($13,000 - 2x) = $730.
0.11x + $120 + $520 - 0.08x = $730.
0.11x - 0.08x + $640 = $730.
0.03x = $730 - $640.
0.03x = $90.
x = $90 / 0.03.
x ≈ $3,000.
So, Aimee invested $3,000 in municipal bonds. The amount invested in mutual funds is x + $2,000 = $3,000 + $2,000 = $5,000. The remaining amount invested in money market accounts is $15,000 - (x + x + $2,000) = $15,000 - (2x + $2,000) = $15,000 - 2($3,000) - $2,000 = $7,000.
Therefore, Aimee invested $3,000 in municipal bonds, $5,000 in mutual funds, and $7,000 in money market accounts.