The current annual interest rate for a short-term (<3 years) period, which fits a 6-month deposit, is about 4.00% compounded continuously as of September 2025. Using this rate, the interest earned on a $30,000 deposit for six months (0.5 years) with continuous compounding can be calculated with the formula:
A=PertA=Pe^{rt}A=Pert
where
- P=30000P=30000P=30000,
- r=0.04r=0.04r=0.04,
- t=0.5t=0.5t=0.5 years,
- eee is the base of the natural logarithm.
Next, the interest earned is A−PA-PA−P. I will calculate this for you.import
math P = 30000 # Principal amount
r = 0.04 # Annual interest rate (continuous compounding)
t = 0.5 # Time in years (6 months)
Calculate the amount with continuous compounding
A = P * math.exp(r * t)
Calculate the interest earned
interest_earned = A - P
interest_earnedThe interest earned on a $30,000 deposit for six months at an
annual interest rate of 4.00% compounded continuously is approximately
$609.51. This was calculated using the continuous compounding formula
A=PertA=Pe^{rt}A=Pert with P=30,000P=30,000P=30,000, r=0.04r=0.04r=0.04, and
t=0.5t=0.5t=0.5 years, then subtracting the principal from the amount to get
the interest earned.
