Question

An investment advisor invested &14,000 in tow accounts. One investment earned 8% annual simple interest. And the other 6.5% annual simple interest. The amount of interest earned for 1 year was $1,027 how much was invested

Answer 1

Investor invested $7,800 at 8% and $6,200 at 6.5%

Explanation:

Use formula

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

where

I = interest

P = principal

r = rate (as decimal)

t = time

First investment:

`P_1=x\\ \\r_1=0.08\\ \\t_1=1`

then

`I_1=x\cdot 0.08\cdot 1\\ \\I_1=0.08x`

Second investment:

`P_2=14,000-x\\ \\r_2=0.065\\ \\t_2=1`

then

`I_2=(14,000-x)\cdot 0.065\cdot 1\\ \\I_2=0.065(14,000-x)`

The amount of interest earned for 1 year was $1,027, then

`I_1+I_2=1,027\\ \\0.08x+0.065(14,000-x)=1,027\\ \\0.08x+910-0.065x=1,027\\ \\0.08x-0.065x=1,027-910\\ \\0.015x=117\\ \\x=7,800\\ \\14,000-x=6,200`

Investor invested $7,800 at 8% and $6,200 at 6.5%