The formula for calculating the ending balance of the certificate of deposit is
A = P × (1 + r/n)^nt
Where:
P = initial deposit amount
r = annual nominal interest rate
t = number of years
n = number of compounding periods per year (for example, 12 for monthly compounding)
A = ending balance
So in the problem:
P = $5,000
r = 0.06 or 6%
n = 2 since it is semi-annual.
t = 5 years
Solution:
A = P × (1 + r/n)^nt
= 5000 x (1 + 0.06/2)^2(5)
= 5000 x (1.03)^10
= 5000 x 1.343916379
= $6,719.58 is the value of the certificate after 5 years.
