Find the value of $1000 deposited for 8 years in an account interest compounded semiannually.
What was the rate of interest ?
To find the value of $1000 deposited for 8 years with semiannual compounding, we'll use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In the given scenario, $1000 is deposited for 8 years, and the interest is compounded semiannually (twice a year). The annual interest rate is not provided, so let's assume it is 5% (0.05 as a decimal).
Now, we can substitute the values into the formula:
A = 1000(1 + 0.05/2)^(2*8)
Simplifying:
A = 1000(1 + 0.025)^(16)
A = 1000(1.025)^(16)
A ≈ 1000(1.432249372)
A ≈ $1432.25
Therefore, the value of $1000 deposited for 8 years with semiannual compounding and an assumed annual interest rate of 5% would be approximately $1432.25.