Question

Tom invested $13,232 part at 9% simple interest and part at 3% simple interest for a period of one year how much did he invest at each rate if each account earn the same interest

Answer 1

Step-by-step explanation:

Let:

x= the money invested at 9% or 0.09 simple interest

y= the money invested at 3% or 0.03 simple interest

The total amount invested for the two investments is $13,232. So,

x+y=13232

or

y=13232-x

We use the formula for simple interest:

I=Prt

Where:

P=Principal Amount

r= Rate of Interest

t= Time Period

It is also given that each account earn the same interest.So,

Interest rate at 9% = Interest rate at 3%

0.09x(1) = 0.03(13232-x)(1)

Simplify and rearrange

0.09x=396.96-0.03x

0.09x+0.03x=396.96

0.12x=396.96

x=396.96/0.12

Calculate

x=3308

Substitute x=3308 into x+y=13232.

`\begin{gathered} x+y=13232 \\ 3308+y=13232 \\ \text{Simplify and rearrange} \\ y=13232-3308 \\ y=9924 \end{gathered}`

Therefore, he invested $3308 at 9% and $9924 at 3%.