Question

Which of the following statements is true?

Options:
There is a relationship between the future value of investment and the effect of compounding frequency. At high-interest rates, increases in compounding frequency will decrease the future value.
Regardless of the value of the interest rate, increasing the compounding frequency will increase the future value.
There is a relationship between the future value of investment and the effect of compounding frequency. At low-interest rates, increases in compounding frequency will decrease the future value.
Regardless of the value of the interest rate, increasing the compounding frequency will decrease the future value.

Answer 1

The true statement is that no matter what the interest rate, increasing the compounding frequency will increase the future value of an investment due to the effects of compound interest.

Step-by-step explanation:

The correct statement is: Regardless of the value of the interest rate, increasing the compounding frequency will increase the future value.

Compound interest is calculated on the principal amount as well as the accumulated interest over past periods, and this effect can cause the future value of investments to grow dramatically over time. The relationship between compound interest and compounding frequency indicates that more frequent compounding periods results in greater accumulation of interest, given a constant interest rate.

As compound interest is the difference between the future value and the present value, using the formula Future Value = Principal x (1 + interest rate)^time, we can see that increasing the frequency of compounding (which is implicitly included in the 'time' exponent when compounding multiple times per year), will increase the future value of the investment.