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

P = Po(1+r)^n.

Po = $200.00

r = (5%/100%) = 0.05 = Annual % rate
expressed as a decimal.

n = 1Comp/yr * 8yrs = 8 Compounding
periods.

Plug the above values into the given Eq and get:

P = $295.49.

To calculate the account balance on January 1, 2005, let's follow these steps:

Step 1: Calculate the number of years between January 1, 1997, and January 1, 2005.
Years = 2005 - 1997 = 8 years

Step 2: Use the compound interest formula to calculate the account balance.

Formula: A = P(1 + r/n)^(nt)
Where:
A = final account balance
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

Given:
P = $200.00
r = 5% or 0.05 (converted to decimal)
n = 1 (compounded annually)
t = 8 years

Plugging in the values:

A = 200(1 + 0.05/1)^(1*8)
A = 200(1 + 0.05)^8
A = 200(1.05)^8
A = 200(1.3943)
A = $278.86 (rounded to two decimal places)

Therefore, the account balance on January 1, 2005, will be approximately $278.86.

To calculate the account balance on January 1, 2005, we need to determine the interest earned each year for the given period and add it to the initial deposit.

First, let's break down the information provided:

- Initial deposit: $200.00
- Interest rate: 5% compounded annually
- Interest compounding period: December 31 of each year
- Time period: January 1, 1997, to January 1, 2005

To calculate the interest earned each year, we will use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = Final account balance
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years

In this case, the interest is compounded annually, so n = 1.

Now, let's calculate the account balance step by step:

Year 1 (January 1, 1997, to December 31, 1997):
A = $200(1 + 0.05/1)^(1*1) = $200(1.05) = $210.00

Year 2 (December 31, 1997, to December 31, 1998):
A = $210.00(1 + 0.05/1)^(1*1) = $210.00(1.05) = $220.50

Year 3 (December 31, 1998, to December 31, 1999):
A = $220.50(1 + 0.05/1)^(1*1) = $220.50(1.05) = $231.53

Year 4 (December 31, 1999, to December 31, 2000):
A = $231.53(1 + 0.05/1)^(1*1) = $231.53(1.05) = $243.10

Year 5 (December 31, 2000, to December 31, 2001):
A = $243.10(1 + 0.05/1)^(1*1) = $243.10(1.05) = $255.26

Year 6 (December 31, 2001, to December 31, 2002):
A = $255.26(1 + 0.05/1)^(1*1) = $255.26(1.05) = $268.02

Year 7 (December 31, 2002, to December 31, 2003):
A = $268.02(1 + 0.05/1)^(1*1) = $268.02(1.05) = $281.42

Year 8 (December 31, 2003, to December 31, 2004):
A = $281.42(1 + 0.05/1)^(1*1) = $281.42(1.05) = $295.49

Year 9 (December 31, 2004, to January 1, 2005):
A = $295.49(1 + 0.05/1)^(1*1) = $295.49(1.05) = $310.27

Therefore, the account balance on January 1, 2005, would be approximately $310.27.