Question

All else equal, fewer compounding periods results in which of the following?

A) lower future values
B) lower present values
C) higher effective annual rates
D) larger number of periods per year

Answer 1

Fewer compounding periods result in lower future values.

Step-by-step explanation:

If all else is equal, fewer compounding periods result in lower future values. This can be explained using the formula for compound interest: A = P(1 + r/n)^(NT), where A is the future value, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

If we decrease the number of compounding periods (n), the term (1 + r/n)^(nt) will become smaller. Since this term is multiplied by the principal (P), the future value (A) will also be smaller than if there were more compounding periods.

For example, consider a situation where you invest $1000 at an annual interest rate of 5% for 1 year. If the interest is compounded annually, the future value will be $1050. However, if the interest is compounded semi-annually (2 compounding periods per year), the future value will be $1051.25. The future value is higher when there are more compounding periods.