Answer:
Explanation:
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According to The Calculator Site, the formula for compound interest is:
A = P (1 + r/n)^nt
where
A = future value of the investment
P = principal amount
r = annual interest rate (decimal)
n = number of times interest is compounded per year
t = time in years
To find the total interest earned, we need to subtract the principal amount from the future value. The formula for total interest is:
I = A - P
where
I = total interest
Now, we can plug in the given values into the formulas. We have:
P = $1,450
r = 0.05
n = 2 (semiannually means twice a year)
t = 15 (from January 2003 to December 2017)
First, we calculate the future value using the compound interest formula:
A = P (1 + r/n)^nt
A = 1450 (1 + 0.05/2)^(2 x 15)
A = 1450 (1.025)^30
A = 1450 x 2.098
A = $3042.10
Then, we calculate the total interest by subtracting the principal amount from the future value:
I = A - P
I = 3042.10 - 1450
I = $1592.10
Therefore, the total interest earned by the end of December in 2017 is $1592.10.