I need to determine the amount of an investment if $1000 is invested at an interest rate of 8% compounded quarterly for 2 years. - Not quite sure how to go about this and would appreciate help. Thank you in advance.
8% compounded quarterly ---> quarterly rate of 2% or .02
number of quarters in 2 years = 8
amount = 1000(1.02)^8 = $ 1171.66
Smacking my forehead!!! ~ Thank you, Reiny, so much for your help!! ~ Two more days and finals will be behind me and i can move on! :)
To determine the amount of an investment, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In your case, the principal amount (P) is $1000, the annual interest rate (r) is 8% (or 0.08 as a decimal), the number of times interest is compounded (n) is 4 (since it's compounded quarterly), and the number of years (t) is 2.
Substituting these values into the formula, we get:
A = 1000(1 + 0.08/4)^(4*2)
Now let's solve it step by step:
First, let's simplify the fractional part within the parentheses:
A = 1000(1 + 0.02)^(4*2)
Next, let's simplify the expression within the parentheses:
A = 1000(1.02)^(4*2)
Now let's calculate the exponent:
A = 1000(1.02)^8
Raise 1.02 to the power of 8:
A = 1000(1.1716197)
Finally, multiply 1000 by 1.1716197 to find the future value:
A ≈ $1,171.62
So, if $1000 is invested at an interest rate of 8% compounded quarterly for 2 years, the amount of the investment after 2 years would be approximately $1,171.62.