Patricia invests $1400 in one account and $1800 in an account paying 4% higher interest. At the end of one year she had earned $232 in interest. At what rates did she invest?

Question

Patricia invests $1400 in one account and $1800 in an account paying 4% higher interest. At the end of one year she had earned $232 in interest. At what rates did she invest?

$1400 invested at ___%

$1800 invested at ___%

Answer 1

1400*int+1800*(int+.04)=232

int=.05

The proper formula to use for int is:

fv=p(1+int/c)^(cn)

future value

principal

int

compound

years

Answer 2

Hi Destiny H

$1400 at 5%

$1800 at 9%

Let x = interest rate for the $1400

Let y = interest rate for the $1800

Total Interest earned = $232

We can start with a basic equation

1400x + 1800 y = 232

We are given that Patricia invests $1400 in one account and $1800 in an account paying 4% higher interest. I am assuming that means 4% higher than the rate for the $1400 and do correct me if I've made the wrong assumption. With that said, we can make the following substitution

y = x + 4%

We can plug in the substitution and get everything in terms of x then solve for x; of course remember to write the percent as a decimal in the calculation below

1400x + 1800( x + .04) = 232

1400x + 1800x + 72 = 232

Combine like terms

3200x + 72 = 232

Subtract 72 from both sides of the equation

3200x = 160

Divide both sides by 3200 to solve for x

x = 160/3200 = .05

x = .05

y = x + .04 = .09

Checking

1400x + 1800y = 232

1400(.05) + 1800(.09) = 232

70 + 162 = 232

232 = 232

I hope you find this useful please send me an email if you have any questions