You inherit one million dollars. You invest it all in three accounts for one year. The first
account pays compounded annually, the second account pays compounded
annually, and the third account pays compounded annually. After one year, you earn
in interest. If you invest four times the money into the account that pays
compared to , how much did you invest in each account?
Investment in the account is
Investment in the account is
Investment in the account is

Ask by Wagner Murphy. in the United States

Mar 21,2025

Question

You inherit one million dollars. You invest it all in three accounts for one year. The first
account pays compounded annually, the second account pays compounded
annually, and the third account pays compounded annually. After one year, you earn
in interest. If you invest four times the money into the account that pays
compared to , how much did you invest in each account?
Investment in the account is
Investment in the account is
Investment in the account is

Ask by Wagner Murphy. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

Let 
- $$ x $$ be the amount invested at $$ 4\% $$,
- $$ y $$ be the amount invested at $$ 5\% $$,
- $$ z $$ be the amount invested at $$ 3\% $$.

We are given three conditions:

1. The total investment is one million dollars:
   $$
   x + y + z = 1,\!000,\!000.
   $$

2. The total interest earned after one year is \$44,000:
   $$
   0.04x + 0.05y + 0.03z = 44,\!000.
   $$

3. The investment in the $$ 4\% $$ account is four times that in the $$ 3\% $$ account:
   $$
   x = 4z.
   $$

**Step 1. Substitute $$ x = 4z $$ into the total investment equation**

$$
4z + y + z = 1,\!000,\!000 \quad \Longrightarrow \quad 5z + y = 1,\!000,\!000.
$$
Thus, 
$$
y = 1,\!000,\!000 - 5z.
$$

**Step 2. Substitute $$ x = 4z $$ into the interest equation**

$$
0.04(4z) + 0.05y + 0.03z = 44,\!000.
$$
Simplify:
$$
0.16z + 0.05y + 0.03z = 44,\!000 \quad \Longrightarrow \quad 0.19z + 0.05y = 44,\!000.
$$

**Step 3. Substitute $$ y = 1,\!000,\!000 - 5z $$ into the interest equation**

$$
0.19z + 0.05(1,\!000,\!000 - 5z) = 44,\!000.
$$
Distribute $$ 0.05 $$:
$$
0.19z + 50,\!000 - 0.25z = 44,\!000.
$$
Combine like terms:
$$
-0.06z + 50,\!000 = 44,\!000.
$$

**Step 4. Solve for $$ z $$**

Subtract $$ 50,\!000 $$ from both sides:
$$
-0.06z = 44,\!000 - 50,\!000 = -6,\!000.
$$
Divide by $$-0.06$$:
$$
z = \frac{-6,\!000}{-0.06} = 100,\!000.
$$

**Step 5. Calculate $$ x $$ and $$ y $$ using $$ z $$**

Since $$ x = 4z $$:
$$
x = 4(100,\!000) = 400,\!000.
$$

And since $$ y = 1,\!000,\!000 - 5z $$:
$$
y = 1,\!000,\!000 - 5(100,\!000) = 1,\!000,\!000 - 500,\!000 = 500,\!000.
$$

**Final Answer**

- Investment in the $$ 4\% $$ account is $$ \$400,\!000 $$.
- Investment in the $$ 5\% $$ account is $$ \$500,\!000 $$.
- Investment in the $$ 3\% $$ account is $$ \$100,\!000 $$.
Investment in the $$ 4\% $$ account is \$400,000. Investment in the $$ 5\% $$ account is \$500,000. Investment in the $$ 3\% $$ account is \$100,000.

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