Question

1)How much does Juan need to invest in each account to earn 8100 per year? include units Juan needs to invest___ in the account paying 3% interest and ___ in the account paying 4% interest

Answer 1

Juan's total money available is $250,000. He wants to invest in two accounts which we shall call A and B.

Therefore, we can say that

`a+b=250000`

Investment A would yield a 3% interest while investment B would yield a 4% interest. Both interests at the end of the year hould total 8,100.

Therefore, we can also say that;

`0.03a+0.04b=8100`

We now have a system of simultaneou equations which we shall solve as follows;

`\begin{gathered} a+b=250000---(1) \\ 0.03a+0.04b=8100---(2) \\ From\text{ equation (1), let a=250000-b} \\ \text{Substitute for a into equation (2)} \\ 0.03(250000-b)+0.04b=8100 \\ 7500-0.03b+0.04b=8100 \\ 7500+0.01b=8100 \\ \text{Subtract 7500 from both sides;} \\ 0.01b=600 \\ \text{Divide both sides by 0.01} \\ b=60000 \end{gathered}`

Therefore, invetment B is $60,000.

Having been given that the total investment is $250,000, then we can derive investment A as follows;

`\begin{gathered} a+b=250000 \\ \text{When b=60000} \\ a+60000=250000 \\ \text{Subtract 60000 from both sides} \\ a=190000 \end{gathered}`

ANSWER:

Juan needs to invest $190,000 in the account paying 3% interest and $60,000 in the account paying 4% interest.