Answer:
The annual interest rate is 41.7%.
Step-by-step explanation:
Given : If a $1,200 investment earns $210 over 5 years.
To find : What is the annual interest rate?
Solution :
Using compound interest formula,
[tex]A=P(1+r)^t[/tex]
Where, A=$1200 is the amount
P=$210 is the principal
t=5 years is the time
r is the interest rate.
Substitute the value,
[tex]1200=210(1+r)^5[/tex]
[tex]\frac{1200}{210}=(1+r)^5[/tex]
[tex]5.714=(1+r)^5[/tex]
Taking 5th root both side,
[tex]\sqrt[5]{5.714}=(1+r)[/tex]
[tex]1.417=(1+r)[/tex]
[tex]r=1.417-1[/tex]
[tex]r=0.417[/tex]
Interest rate in percentage, [tex]r=0.417\times 100=41.7\%[/tex]
The annual interest rate is 41.7%.
