Bob Bryan made deposits of $10,000 at the end of each quarter to Lion Bank, which pays 8% interest compounded quarterly. After 9 years, Bob made no more deposits. What will be the account's balance 4 years after the last deposit? (p. 317)
To find the account's balance 4 years after the last deposit, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final account balance
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case,
P = $10,000 (each deposit)
r = 8% = 0.08 (8% expressed as a decimal)
n = 4 (compounded quarterly)
t = 9 years (since Bob made deposits for 9 years)
First, we need to calculate the future value of the account after 9 years, considering the deposits made:
Future Value = $10,000(1 + 0.08/4)^(4 * 9)
Future Value = $10,000(1 + 0.02)^36
Future Value = $10,000(1.02)^36
Future Value ≈ $20,187.42
Now, let's calculate the account balance 4 years after the last deposit:
Account Balance = $20,187.42(1 + 0.08/4)^(4 * 4)
Account Balance = $20,187.42(1 + 0.02)^16
Account Balance = $20,187.42(1.02)^16
Account Balance ≈ $26,335.03
Therefore, the account's balance 4 years after the last deposit will be approximately $26,335.03.