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Marilyn Mallinson invested $30000, part at 6% annual interest and the rest at 7.5% annual interest. Last year she earned $1995 in interest. How much money did she invest at each rate?

User Flybywire
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Answer: she invested $17000 in the account earning 6% annual interest.

she invested $13000 in the account earning 7.5% annual interest.

Explanation:

Let x represent the amount that she invested in the account earning 6% annual interest.

Let y represent the amount that she invested in the account earning 7.5% annual interest.

Marilyn Mallinson invested $30000, part at 6% annual interest and the rest at 7.5% annual interest. This means that

x + y = 30000

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the account earning 6% annual interest.

P = x

R = 6%

T = 1 year

I = (x × 6 × 1)/100 = 0.06x

Considering the account earning 7.5% annual interest,

P = y

R = 7.5

T = 1

I = (y × 7.5 × 1)/100 = 0.075y

Last year she earned $1995 in interest. This means that

0.06x + 0.075y = 1995 - - - - - - - -

Substituting x = 30000 - y into equation 1, it becomes

0.06(30000 - y) + 0.075y = 1995

1800 - 0.06y + 0.075y = 1995

- 0.06y + 0.075y = 1995 - 1800

0.015y = 195

y = 195/0.015 = 13000

x = 30000 - y = 30000 - 13000

x = 17000

User Lukewestby
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