Q:

Avery and Caden have saved $27,000 towards a down payment on a house. They want to keep some of the money in a bank account that pays 2.4% annual interest and the rest in a stock fund that pays 7.2% annual interest. How much should they put into each account so that they earn 6% interest per year

Accepted Solution

A:
Answer:They should put $6750 in the bank account and $20,250 in the stock fund.Step-by-step explanation:Consider the provided information that Avery and Caden have saved $27000.Let x is the money deposit in the bank and y is the money deposit in stock fund.Therefore,x + y = 27000x Β = 27000 - yThe bank account will pay 2.4% annual interest. [tex]\frac{2.4}{100}x+x=1.024x[/tex]Stock fund pays 7.2% annual interest.[tex]\frac{7.2}{100}y+y=1.072y[/tex]Therefore,1.024 x + 1.072 y = 1.06 Γ— 27000Substitute the x Β = 27000 - y in above equation.1.024 (27000 βˆ’ y) + 1.072 y = 1.06 Γ— 2700027648 βˆ’ 1.024 y + 1.072 y = 286200.048 y = 28620-276480.048 y = 972y = 20250Now, substitute the y = 20250 in x Β = 27000 - y.x = 27000 βˆ’ 20250x = 6750Hence, they should put $6750 in the bank account and $20,250 in the stock fund.