When it comes to compounding interest, the frequency at which interest is compounded has a significant impact on the amount of interest accrued over time. Here are the types of compounding periods mentioned in the choices:
- Infinite: This is not a standard term used in finance for compounding periods.
- Quarterly: This means interest is compounded four times a year.
- Constant: This is not typically used to describe compounding frequency.
- Continuous: This implies that interest is compounded an infinite number of times per year, essentially continuously.
- Monthly: This means interest is compounded twelve times a year.
If the number of compounding periods per year increases without bound, we approach a situation where compounding occurs continuously. In continuous compounding, the frequency of compounding leads to the formula [tex]\( A = P e^{rt} \)[/tex], where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial sum of money).
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form).
- [tex]\( t \)[/tex] is the time the money is invested for, in years.
- [tex]\( e \)[/tex] is the base of the natural logarithm, approximately equal to 2.71828.
Therefore, the correct answer is "continuous". The account is said to earn continuous compound interest when the number of compounding periods per year increases without bound.
