Question

If Ben invests $3000 at 4% interest per year, how much additional money must he invest at 5.5 % annual interest to ensure that the interest he receives each year is 4.5 % of the total amount invested?

Answer 1

Answer:

$1500

Step-by-step explanation:

• Investment 1 = $3000
• Interest 1 = 4%
• Investment 2 = x
• Interest 2 = 5.5%
• Total interest = 4.5%

Total interest:

• 3000*0.04 + x*0.055 = (3000+ x)*0.045    ⇒ multiply by 100 both sides
• 3000*4 + 5.5x = 3000*4.5 + 4.5x                ⇒ parenthesis
• 5.5x - 4.5x = 3000(4.5-4)                             ⇒ collect like terms
• x = 3000*0.5                                                ⇒ simplify
• x = 1500                                                        ⇒ answer

Additional money is $1500