To calculate the amount in the account at the end of each year, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = Amount in the account at the end of the specified time period
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years
In this case:
P = $6500
r = 0.06 (6% expressed as a decimal)
n = 1 (compounded once per year)
(a) To find the amount in the account at the end of 1 year, we substitute the given values into the formula:
A = 6500(1 + 0.06/1)^(1*1)
A = 6500(1 + 0.06)^1
A = 6500(1.06)
A = $6890
The amount in the account at the end of 1 year is $6890.
(b) To find the amount in the account at the end of 2 years, we substitute the values into the formula again:
A = 6500(1 + 0.06/1)^(1*2)
A = 6500(1 + 0.06)^2
A = 6500(1.06)^2
A = 6500(1.1236)
A = $7292.40
The amount in the account at the end of 2 years is $7292.40.