Suppose you buy a two-year CD for $10,000 from First Command Bank.
Assume monthly compounding. Use the APR from the below Table 4.1 and the compound interest formula to determine how much interest the CD earns for you at maturity.
The Table says APR is 3.84%
To determine how much interest the CD earns at maturity, we need to use the compound interest formula.
The formula for compound interest is: A = P(1 + r/n)^(nt)
Where:
A = the future value (including interest)
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $10,000, the annual interest rate (r) is 3.84% (0.0384 as a decimal), the number of times interest is compounded per year (n) is 12 (since it's monthly compounding), and the number of years (t) is 2.
Now let's plug in these values into the formula and calculate the interest earned by the CD:
A = 10000(1 + 0.0384/12)^(12*2)
A = 10000(1 + 0.0032)^(24)
A = 10000(1.0032)^(24)
Calculating this value, we find that A ≈ $10,645.46.
To determine the interest earned, we subtract the principal amount from the future value:
Interest earned = A - P
Interest earned = $10,645.46 - $10,000
Interest earned ≈ $645.46
Therefore, the CD earns approximately $645.46 in interest at maturity.