Determine the amount of an investment if $500 is invested at an interest rate of 4.25% compounded quarterly for 12 years.
To determine the amount of an investment, we 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
Given the information:
P = $500
r = 4.25% (or 0.0425 as a decimal)
n = 4 (quarterly compounding)
t = 12 years
Let's plug in these values into the compound interest formula and calculate the future value (A):
A = 500(1 + 0.0425/4)^(4*12)
Now, let's simplify the equation:
A = 500(1.010625)^(48)
Using a calculator or spreadsheet, let's evaluate (1.010625)^48:
(1.010625)^48 = 1.675080095
Now, substitute this value back into the formula:
A ≈ 500 * 1.675080095
A ≈ $837.54
Therefore, the amount of the investment after 12 years would be approximately $837.54.