Question

A portion of $ 100,000 (x) is invested with a 3% after one year. The rest of the investment (and) obtained a return of 1%. The total return on investment was $ 1,800. 1) What equation shows the return on investment? 2) What equation shows how the $ 100,000 was divided?3) how much money was invested at a 3% rate of return?4) how much money was invested at a rate of return of 1%

Answer 1

We can write a system of equations that describe our problem.

Since we don't know how the original $100,000 was divided, we call the two parts X and Y

So we know that X + Y = 100000

Then we know the Combined Interest coming from the accounts.

We use the Interest formula for return on investment:

I = P * r * t

were P is the principal, r is the percent rate (in decimal form), and t is the number of years (in our case 1)

Then the interest from the 3% account (let's call it I1) (if X amount of money was deposited there) is:

I1 = X * 0.03 * 1 = 0.03 X

Similarly, the interest I2 coming from the 1% account (if Y amount of money was deposited there) is given by:

I2 = Y * 0.01 * 1 = 0.01 Y

Then, the addition of these two interest is our total return of $1800:

0.03 X + 0.01 Y = 1800

Then our system of equations is:

X + Y = 100000

0.03 X + 0.01 Y = 1800

which we solve by substituting for example for Y in the first equation:

Y = 100000 - X

and replacing the Y by this expression in our second equation:

0.03 X + 0.01 (100000 - X) = 1800

use distributive property to eliminate parenthesis:

0.03 X + 1000 - 0.01 X = 1800

combine like terms

0.02 X + 1000 = 1800

subtract 1000 from both sides

0.02 X = 800

divide both sides by 0.02 to completely isolate X:

X = 800 / 0.02

X = $40000

This is the amount deposited on the 3% account

Then we easily calculate the amount deposited in the other account by replacing x with $40000 in the equation we use for substitution:

Y = $100000 - $40000 = $60000

Then, the amount deposited in the 1% account was $60000

and the amount deposited in the 3% account was $40000.