Question

Enter the correct answeach column.5. Bellatrix Lestrange keeps her money in GringottsWizarding Bank. She decided to take $100,000out of her vault and split it among three differentaccounts. She placed part in a savings accountpaying 3% per year, twice as much in Wizard bondspaying 5.5%, and the rest in a mutual fund thatreturned 4%. Her income from these investmentsafter one year was $4,480. How much did Bellatrixplace in each account?11223334.44HOW MUCH DID BELLATRIX PLACE IN THEMUTUAL FUND?556670N (0088

Answer 1

Assum,e that she put x in the account of 3%

So in wizard bonds, she put twice so it is 2x

The rest in the account of 4%

The rest is 100,000 - x - 2x = 100,000 - 3x

The rule of the investment is :

`I=\text{prt}`

I is the interest, P is the money she invested, r is the rate and t is the time

We will make equation for each account

`\begin{gathered} I_1=x((3)/(100))(1)=0.03x_{} \\ I_2=(2x)((5.5)/(100))(1)=0.11x \end{gathered}`
`I_3=(100,000-3x)((4)/(100))(1)=4000-0.12x`

The sum of the interest is 4,480, so add them and equate the sum by 4,480 to find the value of x

0.03x + 0.11x + 4000 - 0.12x = 4,480

Add like terms in the left side

0.02x + 4000 = 4,480

Subtract 4000 from both sides

0.02x + 4000 - 4000 = 4,480 - 4000

0.02x = 480

Divide both sides by 0.02

x = 24,000

The value in the mutual fund is 100,000 - 3x, so substitute s by 24,000

The mutual fund = 100,000 - 3(24,000) = 100,000 - 72,000 = 28,000

The mutual fund = $28,000