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Question

a small company invested 50000 into two accounts; a savings account that earned 3.9% annual simple interest adn in a stockfun that earned 10.5% annual simple interest. If the company earned $2940 interest annually from the investments, how mush was in each accoun

Answer 1

Hi Amber,

Let's begin by writing algebraic expressions to represent the amount invested in each account:
    x = invested amount in account earning 3.9% interest annually
    50000 - x = remainder invested in other account earning 10.5% interest annually

Next, let's write the Simple Interest formula and identify its variables:
    i = prt (Simple Interest formula)
         i (interest amount)
         p (principal amount, i.e. invested amount)
         r (interest rate)
         t (time in years)

Next, let's write an equation to express the sum of the earned interest amounts at each rate as being equal to the annual total earned interest amount:
    I (at 3.9%) + I (at 10.5%) = Total I
    (x)(0.039)(1) + (50000 - x)(0.105)(1) = 2940

Next, let's solve our equation to determine the invested amount in each account:
    (x)(0.039)(1) + (50000 - x)(0.105)(1) = 2940
    0.039x + (50000 - x)(0.105) = 2940
    0.039x + 5250 - 0.105x = 2940
    -0.066x + 5250 = 2940
    -0.066x = 2940 - 5250
    -0.066x = -2310

     x = -2310/-0.066

     x = $35000 (invested amount in account earning 3.9% interest annually)

     50000 - x = 50000 - 35000

     50000 - x = $15000 (remainder invested in other account earning 10.5% interest annually)

We can verify our answers for the invested amounts in each account by plugging them back into our equation and seeing if the sum of their earned interest amounts is equal to the annual total earned interest amount:
    (x)(0.039)(1) + (50000 - x)(0.105)(1) = 2940
    (35000)(0.039) + (15000)(0.105) = 2940
    1365 + 1575 = 2940

    $2940 = $2940 (sum = total; answers verified)

Thanks for submitting this problem and glad to help.

God bless, Jordan (Romans 5:8)