r=0.57%
Step-by-step explanation:
if $5700 is invested in a savings account which interest is compounded annually
$5700 turns into $6100 in 12 years
Compound interest formula is
[tex]A= P (1+r)^t[/tex]
P is the principal
r is the rate of interest
t is the time period
A is the amount in account after t years
P= 5700, A= 6100, t=12
[tex]6100= 5700 (1+r)^12[/tex]
divide by 5700 on both sides
[tex]\frac{61}{57} =(1+r)^{12}[/tex]
take 12th root on both sides
[tex]\sqrt[12]{\frac{67}{51}} =1+r[/tex]
now subtract 1 on both sides
[tex]\sqrt[12]{\frac{67}{51}}-1 =r[/tex]
r=0.00567
to get interest rate in percentage we multiply by 100
r=0.00567 * 100= 0.57%
