on january 1,1997 you deposit $200.00 in a bank account paying 5% interest compunded annually on december 31 of each year. which of the following will be the account balance on january 1,2005
looks like you money sat there for 8 years
amount = 200(1.05)^8 = .....
that equals 295.49 right?
To calculate the account balance on January 1, 2005, we need to take into account the initial deposit, the interest rate, and the compounding period.
The formula for calculating compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final account balance
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Given the information in the question, we have:
P = $200.00
r = 5% (0.05 as a decimal)
n = 1 (compounded annually)
t = 2005 - 1997 = 8 years
Plugging in the values into the formula, we get:
A = 200(1 + 0.05/1)^(1*8)
A = 200(1 + 0.05)^8
A = 200(1.05)^8
A ≈ 200(1.4693)
A ≈ $293.86
Therefore, the account balance on January 1, 2005, would be approximately $293.86.