Answer:
[tex]r=10\%[/tex]
Step-by-step explanation:
The correct question is
A bank says you can double your money in 10 years if you put $1,000 in a simple interest account. What annual interest rate does the bank pay?
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=10\ years\\ P=\$1,000\\ A=\$2,000\\r=?[/tex]
substitute in the formula above
[tex]2,000=1,000(1+10r)[/tex]
Solve for r
Divide by 1,000 both sides
[tex]2=1+10r[/tex]
Subtract 1 both sides
[tex]10r=2-1[/tex]
[tex]10r=1[/tex]
Divide by 10 both sides
[tex]r=1/10[/tex]
[tex]r=0.10[/tex]
Convert to percentage (multiply by 100)
[tex]r=0.10*100=10\%[/tex]
