Question

susan invests 2 times as much money at 12 % as she does at 9 % . if her total interest after 1 year is $ 1980 , how much does she have invested at each rate?

Answer 1

She has invested $6000 at 12% and $12,000 at 9% rate.

Let x stand in for the amount she put into the account that earned 12% interest.

Let y stand in for the amount she put into the account that earned 9% interest.

At 12%, Susan invests twice as much as she does at 9%. It follows that

x =2y

The calculation of simple interest follows the following formula:

I = $\frac{P X R X T}{100}$

Taking into mind the account's 12% interest rate,

P = x, T = 1 year, R = 9℅

I = (x × 9 × 1)/100 = 0.09x

Taking into mind the account's 9% interest rate,

P = y, T = 1 year, R = 5℅

I = (y × 5 × 1)/100 = 0.05y

If after a year her total interest is $1980, it means that

0.12x + 0.09y = 1980    (equation 1)

When x = 2y is substituted into equation 1, it results in

0.12x × 2y + 0.09y = 1980

0.24y + 0.09y = 1980

0.33y = 1980

y = 1980/0.33

y = 6000

x = 2y = 2 × 6000

x = 12000

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