Question

Esmeralda invests $1100 in one account and $1600 in an account paying 2% higher interest. At the end of one year she had earned $248 in interest. At what rates did she invest?

Answer 1

Equations

We'll apply equations to a financing situation.

The interest earned in one year when investing P dollars at a rate r is:

I = P.r

The first investment is P1 = $1100 at a rate r (unknown so far), so the interest is:

I1 = 1100.r

The second investment is P2=$1600 at a rate 2% higher, that is, at r + 0.02. Thus the interest is:

I2 = 1600 (r + 0.02)

The sum of the interests is:

1100r + 1600 (r + 0.02) = 248

That is the equation to solve. Perform the product and eliminate parentheses:

1100r + 1600r + 32 = 248

Simplify:

2700r + 32 = 248

Subtract 32:

2700r = 216

Finally, divide by 2700:

r = 216 / 2700

r = 0.08

The first investment was done at 8% and the second at 8+2 = 10%