Question

You inherit 70,000 from a very wealthy grandparent, with the stipulation that for the 1st yr, the money must be invested in two stocks paying 4% and 10% annual interest, respectively. How much should be invested at each rate if the total interest earned for the yr is 4,000?

40,000 invested at 4% 30,000
30,000 invested at 4% 40,000
50,000 invested at 4% 20,000
20,000 invested at 4% 50,000

Answer 1

how is this setup?

Answer 2

this is pretty simple. lets go through all the options. what is the first option?
40000 invested at 4% and 30000 invested at 10% right?
so add up the returns. what is 4% of 40000 added to 10% of 30000?

Answer 3

3000+1600

Answer 4

so that is 4600 total return. but the problem says that the return was only 4000. so option A is wrong. similarly work it out for the other options

Answer 5

awesome, but i was looking for an algebraic solution, not a brute force. :)

Answer 6

okay. lets go for the algebraic version. lets say he invests x amount of money at 4%. that means that he invests 70000-x amount of money at 10%. the total return is 4000. so can you write an expression for this?

Answer 7

4000=70000-x*.1*1

Answer 8

why are you multiplying 0.1 and 1? what does that accomplish?

Answer 9

I=Prt

Answer 10

okay, but that still accounts for only the investment of 70000-x invested at 10 percent. what about the other part?

Answer 11

that is the heart of my question. how do i relate the two together?

Answer 12

i = prt right? so i = (70000-x)*0.1*1 is the interest on the 70000-x. so lets call that interest i1.
what is the interest on the 4% investment? call it i2.

Answer 13

i2=(70000-x)*0.04*1

Answer 14

i1+i2 = 4000

Answer 15

no. if you invest 70000 - x at 10%, that means you invest x at 4% since x + 70000-x = 70000, right?

Answer 16

ok

Answer 17

i2=x*0.04*1

Answer 18

okay that's good. excellent job. so i1 = (70000-x) * 0,1 * 1
and i2 = x * 0.04 * 1.
but as you pointed out earlier, i1 + i2 = 4000. so what does that mean? can you combine everything and write down the equation?

Answer 19

(70000-x) * 0.1 + 0.04x = 4000

Answer 20

very good! now solve for x. keep in mind that x is the amount of money ivested at 4%

Answer 21

50000 at .04 and 20000 at .1 fantastic thanks!!!

Answer 22

great! good job!

Answer 23

high five!