today Thomas deposited $100,000 in a three-year,12% CD that compounds quartly. What is the maturity value of the CD?
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To calculate the maturity value of the CD, we need to use the formula for compound interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = Maturity value of the CD
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case,
P = $100,000
r = 12% = 0.12 (as a decimal)
n = 4 (quarterly compounding)
t = 3 years
Plugging in the values into the formula, we can calculate the maturity value:
A = $100,000 * (1 + 0.12/4)^(4*3)
First, divide the annual interest rate (0.12) by the number of times interest is compounded per year (4). This gives us 0.03.
Next, multiply the number of times interest is compounded per year (4) by the number of years (3) to get 12.
Now, add 1 to the result from the first step (0.03) to get 1.03.
Raise 1.03 to the power of 12 to get 1.42517.
Finally, multiply the principal amount ($100,000) by the result from the previous step (1.42517) to calculate the maturity value:
A = $100,000 * 1.42517 = $142,517.
Therefore, the maturity value of Thomas's CD after three years would be $142,517.