Question

Caryn earned $5000 working part time as a cashier in a department store. She put her earnings into three different bank accounts. She put some of her money in a checking account paying 5% annual interest, some in a savings account paying 6%, and the rest in a 1-year certificate of deposit paying 7%. The accounts earned simple interest. No additional money was deposited into or withdrawn from the accounts during the year, and the total interest at the end of the year was $325. If she invested 3 times as much at 6% as at 5%, find the amount she invested at each rate.

Answer 1

Caryn invested $x in the checking account at 5% annual interest, $3x in the savings account at 6% annual interest, and $5000 - $4x in the certificate of deposit at 7% annual interest. The total interest earned at the end of the year was $325.

Step-by-step explanation:

Let's say Caryn invested $x in the checking account at 5% annual interest. She invested 3 times as much, so she invested $3x in the savings account at 6% annual interest. The rest of her money, which is $5000 - $x - $3x = $5000 - $4x, she invested in the certificate of deposit at 7% annual interest.

The total interest earned at the end of the year was $325.

Using the formula for simple interest:

Total interest = Principal × Rate × Time

For the checking account:

Interest from checking account = $x × 0.05 × 1 = 0.05x

For the savings account:

Interest from savings account = $3x × 0.06 × 1 = 0.18x

For the certificate of deposit:

Interest from certificate of deposit = ($5000 - $4x) × 0.07 × 1 = 0.07(5000 - 4x)

According to the given information, the total interest is $325. So we can write the equation:

0.05x + 0.18x + 0.07(5000 - 4x) = 325

Solve this equation to find the value of x, and then calculate the investments in each account.