Question

Mrs. Ming invested an amount of money in two accounts for one year. She invested some at 8% interest and the rest at 6% interest. Her total amount invested was $1,500. At the end of the year, she had earned $106. 40 in interest. How much had Mrs. Ming invested in the account paying 6%? $117 $680 $760 $820.

Answer 1

Interest rate for one year is rate percent amount of original investment. The amount invested by Mrs. Ming in the account paying 6% was $680

How to calculate interest after 1 year if the rate of interest is R% annually?

Suppose that annually there is interest rate of R%. The amount initially invested is P, then for 1 year, it doesn't matter if its simple or compounding annually, the interest is same (it doesn't remain same if compounding isn't annually or if the time is > 1 year)

The interest for 1 year will be $\dfrac{P}{100} \times R$

Let we have the initial amount spent in account paying 8% interest rate as $x

Let for 6% interest paying account, initial amount was $y

Then, by the given data, we have:

$x + y = 1500$

and

$\dfrac{x}{100} \times 8 + \dfrac{y}{100} \times 6= 106.40\\\\8x + 6y = 10640\\4x + 3y = 5320$

Thus, we got a system of linear equations as :

$x + y = 1500\\4x + 3y = 5320$

From equation 1, getting value of x in terms of y, we get:

$x = 1500 - y$

Substituting this value in second equation, we get:

$4x + 3y = 5320\\4(1500-y) +3y = 5320\\6000 - y = 5320\\y =680$

Putting this value of y in the equation we got for x,

$x = 1500 - y\\x = 1500 - 680= 820$

Thus, amount invested by Mrs Ming in account paying 8% interest rate as $x = $820

and  for 6% interest paying account, initial amount was $y = $680

Thus,

The amount invested by Mrs. Ming in the account paying 6% was $680

Learn more about system of linear equations here:

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