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

Answer:

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

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

Step-by-step 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 $\ 6,000$