trying to find how much was used for investments at varying percentages to get $795 in interest.

Question

A man inested half his money at 5%, 1/3 his money at 4% and the rest at 3.5%. If his total investment income is $795 how much had he invested?

Answer 1

I assume the rates are per annual percentage rates (APR), the interest is simple interest, and the income is yearly income.

 

Interest = P*R*t

 

Where P = principle, r = the APR expressed as a decimal, and t = years.  Since we have three rates and the principle is divided into three parts:

• (1/2)P invested at 5% (0.05)
• (1/3)P invested at 4% ().04)
• (1/6)P (the remainder) invested at 3.5% (0.035)

 

$795 = (1/2)P*(0.05)*(1 year) + (1/3)P*(0.04)*(1 year) + (1/6)P*(0.035)*(1 year)

 

$795 = 0.025P + 0.0133P + 0.0058P

 

Solve for P.