What is the future value of $4000 in a bank for 9 years at 12% compounded semi annually rounded to the nearest cent.
To calculate the future value of an investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment,
P is the principal amount (initial investment),
r is the interest rate (in decimal form),
n is the number of times the interest is compounded per year,
t is the number of years.
Let's plug in the values from your question:
P = $4000
r = 12% = 0.12 (as a decimal)
n = 2 (compounded semi-annually, meaning twice a year)
t = 9 years
Now we can calculate the future value using the formula:
A = 4000(1 + 0.12/2)^(2*9)
First, let's simplify the inside of the parentheses: (1 + 0.12/2) = 1.06
A = 4000 * (1.06)^(2*9)
Next, calculate the exponent: (2*9) = 18
A = 4000 * (1.06)^18
Now, let's calculate the value of (1.06)^18 using a calculator or computer program:
(1.06)^18 = 1.6596202 (rounded to 7 decimal places)
Finally, multiply 4000 by 1.6596202 to find the future value:
A = $6,638.48 (rounded to the nearest cent)
Therefore, the future value of $4000 in a bank for 9 years at 12% compounded semi-annually, rounded to the nearest cent, is $6,638.48.