Answer:
To calculate the balance of the account after the seventh year with a 2.5% annual interest rate compounded annually, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future balance of the account
P = the initial principal (starting amount), which is $10,000 in this case
r = the annual interest rate (in decimal form), which is 2.5% or 0.025
n = the number of times the interest is compounded per year (annually in this case)
t = the number of years
In this scenario, you are compounding annually (n = 1), and you want to find the balance after the seventh year (t = 7). Plugging in these values:
A = 10,000(1 + 0.025/1)^(1*7)
Now, calculate the values within the parentheses:
A = 10,000(1 + 0.025)^7
A = 10,000(1.025)^7
A = 10,000(1.196842)
A ≈ $11,968.42
So, the balance of the account after the seventh deposit will be approximately $11,968.42.