You inherit 9000 with the regulation that for the first year

You inherit $9,000 with the regulation that for the first year the money needs to be invested in two different accounts paying 6% and 8% annual interest, respectively. How much should you invest at each rate if the total interest earned for the entire year is to be $620?

Solution

solution

we invest $9000 in two accounts paying 6% and 8% anual interest. At the end of the year, the total interest from these investments was $620. How much was invested at each rate?

Let x = amount invested at 6%
then because the total invested was $9000 then
9000-x = amount invested at 8%

And, because the total interest amount at the end of the year was $620

.06x + .08(9000-x) = 620

.06x + 720 - .08x = 620
-.02x + 720 = 620
-.02x = -100
x = $5000 (amount invested at 6%)

Amount invested at 8%:
9000-x = 9000-5000 = $4000 (amount invested at 8%)