Question

A mother earned ​$ 18750.00 18750.00 from royalties on her cookbook. She set aside​ 20% of this for a down payment on a new home. The balance will be used for her​ son's future education. She invests a portion of the money in a bank certificate of deposit​ (CD account) that earns​ 4% and the remainder in a savings bond that earns​ 7%. If the total interest earned after one year is ​$ 900.00 900.00​, how much money was invested at each​ rate? How much money was invested in the CD​ account? ​$ nothing ​(Round to the nearest​ cent.)

Answer 1

a) $ 5000, $ 10000 b) $ 5000

Step-by-step explanation:

The royalties money = $18750

She set aside 20% for new home which = 0.2 × 18750 = $ 3750

Amount remaining = 18750 - 3750 = $15000

She invested a sum in a bank certificate of deposit

let the amount invested in bank certificate = y

profit from the investment in the bank = 0.04y

second investment amount = 15000 - y

profit of investment = 0.07 ( 15000 - y)

sum of the two profit = 0.04y + 0.07 (15000 - y) = total profit = $ 900

0.04y + 0.07 (15000 - y) = 900

open the bracket and rearrange the equation

0.04y + 1050 - 0.07y = 900

0.04y - 0.07y = 900 - 1050

-0.03y = -150

divide both side by -0.03

y = -150 / -0.03 = $ 5000

The amount of money invest at 4% is $5000

The amount of money invested at 7% = 15000 - 5000 = $10000

The amount of money invested in CD account = $ 5000