6700 dollars is placed in an account with an annual interest rate of 8%. How much will be in the account after 24 years, to the nearest cent?
We can use the formula for compound interest: A = P(1 + r/n)^(nt), where:
A is the final amount (what we want to find)
P is the principal amount (initial deposit)
r is the annual interest rate (as a decimal)
n is the number of times that interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $6700, the annual interest rate (r) is 8%, and the account compounds once per year (n = 1). Therefore, we can substitute these values into the formula:
A = $6700(1 + 0.08/1)^(1*24)
Simplify the expression inside parentheses:
A = $6700(1 + 0.08)^(24)
Solve the expression inside the parentheses:
A = $6700(1.08)^(24)
Calculate the value of (1.08) raised to the 24th power:
A = $6700(2.20804027)
Multiply $6700 by 2.20804027:
A ≈ $14,774.85
Therefore, there will be approximately $14,774.85 in the account after 24 years.