Question

Amy invests money in two simple interest accounts. She invests four times as much in an account paying 11% as she does in an account paying 5%. If she earns $183.75 in interest in one year from both accounts combined, how much did she invest altogether?

Answer 1

Answer: Total amount invested in both accounts is $1875

Step-by-step explanation:

Let x represent the amount invested at 11%.

Let y represent the amount invested at 5%.

She invests four times as much in an account paying 11% as she does in an account paying 5%. This means that

x = 4y

The formula for determining simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents the rate of investment

T represents the time in years.

Considering the amount invested at 11%,

I = (x × 11 × 1)/100 = 0.11x

Considering the amount invested at 5%,

I = (y × 5 × 1)/100 = 0.05y

If she earns $183.75 in interest in one year from both accounts combined, it means that

0.11x + 0.05y = 183.75 - - - - - - - - - -1

Substituting x = 4y into equation 1, it becomes

0.11 × 4y + 0.05y = 183.75

0.44y + 0.05y = 183.75

0.49y = 183.75

y = 183.75/0.49

y = 375

x = 4y = 375 × 4

x = 1500

Total amount invested in both accounts is

1500 + 375 = $1875