An initial investment of $1000 is appreciated for 8 years in an account that earns 9% interest, compounded annually. Find the amount of money in the account at the end of the period
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To find the amount of money in the account at the end of the 8-year period, we can use the formula for compound interest:
A = P(1 + r/n)^(nt),
where:
A is the final amount of money in the account,
P is the initial investment,
r is the interest rate (expressed as a decimal),
n is the number of times the interest is compounded per year, and
t is the number of years the money is invested for.
In this case, the initial investment (P) is $1000, the interest rate (r) is 9% (or 0.09 as a decimal), the interest is compounded annually (n = 1), and the investment period (t) is 8 years.
Plugging these values into the formula, we get:
A = 1000(1 + 0.09/1)^(1*8).
First, we simplify inside the parentheses:
A = 1000(1.09)^8.
Next, we calculate the exponent:
A = 1000(1.991359977).
Finally, we multiply the initial investment by the calculated value:
A ≈ $1,991.36.
Therefore, the amount of money in the account at the end of the 8-year period is approximately $1,991.36.
The accumulation value at the end of nth
period A=P(1+i)^n
A=1000*1.09^8=1,992.56