Question

An executive invests $25,000, some at 7% and the rest at 4% annual interest. If he receives an annual return of 1,390, how much is invested at each rate

Answer 1

$13,000 at 7% and $12,000 at 4%

Explanation:

Use formula:

`I=P\cdot r\cdot t,`

where

I = interest,

P = principal,

r = rate (as decimal),

t = time (in years)

7% rate:

P = $x

r = 0.07

t = 1 year

Then

`I_1=x\cdot 0.07\cdot 1\\ \\I_1=0.07x`

4% rate:

P = $(25,000 - x)

r = 0.04

t = 1 year

Then

`I_2=(25,000-x)\cdot 0.04\cdot 1\\ \\I_2=0.04(25,000-x)`

If he receives an annual return of $1,390, then

`I_1+I_2=1,390,`

so

`0.07x+0.04(25,000-x)=1,390\\ \\7x+4(25,000-x)=139,000\\ \\7x+100,000-4x=139,000\\ \\7x-4x=139,000-100,000\\ \\3x=39,000\\ \\x=13,000\\ \\25,000-x=25,000-13,000=12,000`