roger fox made deposits of $ 900 semiannualy to Reel Bank which pays 6% interest compounded semiannualy. After seven years, Roger made no more deposits. What would be the ballance in the accounnt eight years later from the last deposit?
To calculate the balance in the account eight years later from the last deposit, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (balance in the account)
P = principal amount (initial deposit)
r = annual interest rate
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount (P) is $900, the annual interest rate (r) is 6%, and the interest is compounded semiannually (n = 2). We need to calculate the balance after seven years, so t = 7.
First, we need to calculate the number of compounding periods (nt):
nt = 2 * 7 = 14
Now, let's substitute the values into the formula and calculate the balance (A) after seven years:
A = $900(1 + 0.06/2)^(14)
A = $900(1.03)^14
A ≈ $1,201.76
After seven years, the balance would be approximately $1,201.76.
To find the balance eight years later from the last deposit, we need to calculate the balance with an additional year added. So, now t = 8:
A = $900(1 + 0.06/2)^(2*8)
A = $900(1.03)^16
A ≈ $1,283.85
Therefore, the balance in the account eight years later from the last deposit would be approximately $1,283.85.