$16,000 is invested for 9 years with an APR of 6% and a quarterly compounding.
what is the balance in the account after 9 years?
To calculate the balance in the account after 9 years with quarterly compounding, we can 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 investment)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case:
P = $16,000
r = 0.06 (6% expressed as a decimal)
n = 4 (quarterly compounding)
t = 9
A = 16000(1 + 0.06/4)^(4*9)
A ≈ 16000(1 + 0.015)^36
A ≈ 16000(1.015)^36
A ≈ 16000(1.671563)
A ≈ $26,744.10
Therefore, the balance in the account after 9 years with an APR of 6% and quarterly compounding is approximately $26,744.10.