Answer:
$4,562.5
Step-by-step explanation:
The amount Arvin has to invest, P = $10,000
The interest paid on the investment in the term deposit = 5%/year
The interest paid om the investment in Canada savings bonds = 3.4%/year
The amount Arvin earned at the of the year as simple interest, A = $413
Let, <em>x</em>, represent the amount Arvin invested in the term deposit and let, <em>y</em>,<em> </em>represent the amount he invested in Canada savings bonds, we can get the following system of equations
x + y = 10,000...(1)
0.05·x + 0.034·y = 413...(2)
Making <em>y</em> the subject of equation (1) and substituting the value in equation (2), we get;
From equation (1), we get, y = 10,000 - x
Plugging the above value of <em>y</em> in equation (2) gives;
0.05·x + 0.034 × (10,000 - x) = 413
∴ 0.05·x - 0.034·x + 340 = 413
x = (413 - 340)/(0.05 - 0.034) = 4,562.5
Therefore, the amount Arvin invested in the term deposit at 5%, x = $4,562.5
<em>(y = 10,000 - x</em>
<em>∴ y = 10,000 - 4,562.5 = 5,437.5</em>
<em>The amount Arvin invested in Canada savings bonds, y = $5,437.5.)</em>
