Question

You invested a total of $9,000 at 4 1/2 % and 5% simple interest. During one year, the two accounts earned $435. How much did you invest in each account

Answer 1

The amount invested at 4.5% was
`\$3,000`

The amount invested at 5% was
`\$6,000`

Explanation:

we know that

The simple interest formula is equal to

`I=P(rt)`

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

Let

x -----> the amount invested at 4.5%

9,000-x -----> the amount invested at 5%

in this problem we have

`t=1\ year\\ P1=\$x\\ P2=\$(9,000-x)\\I=\$435\\r1=0.045\\r2=0.05`

substitute

`435=x(0.045*1)+(9,000-x)(0.05*1)`

`435=0.045x+450-0.05x`

`0.05x-0.045x=450-435`

`0.005x=15`

`x=\$3,000`

so

`9,000-x=\$6,000`

therefore

The amount invested at 4.5% was
`\$3,000`

The amount invested at 5% was
`\$6,000`