Question

If $6300 is invested at 3% annual simple interest, how much should be invested at 9% annual simple interest so that the total yearly income from both investments is $999?

A) $1700 should be invested at 9%.
B) $8000 should be invested at 9%.
C) $5400 should be invested at 9%.
D) $3700 should be invested at 9%.

Answer 1

To achieve a total annual income of $999 with two different simple interest rates, $6300 invested at 3% and $2700 invested at 9%, the correct answer is option A, which describes the amount that needs to be invested at 9%.

Step-by-step explanation:

The correct answer is option A, $1700 should be invested at 9%.

First, calculate the annual simple interest from the $6300 investment at 3%:

Interest = Principal × Rate × Time

Interest = $6300 × 0.03 × 1

Interest = $189

The total yearly income from both investments must be $999, and you already have $189 from the first investment. So, the income needed from the second investment at 9% simple interest is:

$999 - $189 = $810

Let 'P' be the principal amount needed at 9%. Then, use the simple interest formula again:

$810 = P × 0.09 × 1

P = $810 / 0.09

P = $9000

Therefore, $9000 must be the total money invested at both 3% and 9%. Because you already have $6300 at 3%, subtract this from $9000 to find the amount needed at 9%:

$9000 - $6300 = $2700

So, $2700 should be invested at 9% to get a total annual income of $999.