Use the compound interest formula for compounding more than once a year to determine the accumulated balance after the stated period.
$16,000 deposit at an APR of 5% with semiannual compounding for 8 years
To calculate the accumulated balance after 8 years with semiannual compounding, we'll use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated balance
P = Initial deposit (principal) = $16,000
r = Annual interest rate (APR) = 5% = 0.05
n = Number of times interest is compounded per year = 2 (semiannual compounding)
t = Number of years = 8
Plugging in the values, the formula becomes:
A = 16000(1 + 0.05/2)^(2*8)
Simplifying inside the parentheses:
A = 16000(1 + 0.025)^(16)
Calculating the exponent:
A = 16000(1.025)^(16)
Using a calculator or performing the calculation step by step:
A ≈ 16000 * 1.44092469689
A ≈ $23,054.79
Therefore, the accumulated balance after 8 years with semiannual compounding is approximately $23,054.79.