the exponential expression to find the value of the cd, in dollars, after t years will be: ![a= 1500(1.0231)^t](/tex.php?f=a= 1500(1.0231)^t)
step-by-step explanation:
formula of compound interest:
, where
final value after
years,
initial value,
rate of interest in decimal and
number of compounding in a year.
oliver plans to purchase a $1,500 certificate of deposit (cd) at his bank. that means, ![p= 1500](/tex.php?f=p= 1500)
the cd will earn 2.3% interest, compounded semi-annually.
so,
and ![n= 2](/tex.php?f=n= 2)
now, plugging these values into the above formula, we will
![a= 1500(1+\frac{0.023}{2})^2^t \\ \\ a=1500(1.0115)^2^t\\ \\ a= 1500[(1.0115)^2]^t\\ \\ a= 1500(1.0231)^t](/tex.php?f=a= 1500(1+\frac{0.023}{2})^2^t \\ \\ a=1500(1.0115)^2^t\\ \\ a= 1500[(1.0115)^2]^t\\ \\ a= 1500(1.0231)^t)
(rounded to the nearest ten-thousandth)
so, the exponential expression to find the value of the cd, in dollars, after t years will be: ![a= 1500(1.0231)^t](/tex.php?f=a= 1500(1.0231)^t)