Question

Brian has half of his investments in stock paying a 5% dividend and the other half in a stock paying 9% interest. If his total annual interest is $420, how much does he have invested?

Answer 1

The amount invested in each stock, the stock interest rate and the

duration of the investment, determines the interest.

• Brian invested $3,000 in the stock that pays 5% dividend and $3,000 in the stock that pays 9% to make a total investment of $6,000.

Reasons:

Let X represent the sum of the amount Brian invested, we have;

Amount invested in stock paying 5% dividend = $\dfrac{X}{2}$

Amount invested in stock paying 9% dividend = $\dfrac{X}{2}$

Total annual interest = $420

Required:

The amount invested in the stocks

Solution:

The amount invested is found as follows;

$\dfrac{X}{2} \times 5\% + \dfrac{X}{2} \times 9\% = 420$

0.025·X + 0.045·X = 420

0.07·X = 420

$\displaystyle \mathrm{The \ amount \ invested , \, X} = \frac{420}{0.07} = \mathbf{ 6,000}$

The amount he invested = $6,000 ($3,000 in each stock)

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