The future value of a lump-sum investment will increase if you:

• A. Invest a smaller initial amount
• B. Decrease the number of compounding periods
• C. Increase the interest rate
• D. Withdraw funds periodically

Answer: (C)

Verified step by step guidance

1. Understand the concept of future value: Future value (FV) is the value of an investment at a specific point in the future, based on a given interest rate and compounding periods. It is calculated using the formula: ${\mathrm{FV}}_{}=P_{}(1+r_{})n^{}$, where P is the principal amount, r is the interest rate per period, and n is the number of compounding periods.
2. Analyze the impact of increasing the interest rate: When the interest rate (r) increases, the term $(1+r_{})$ becomes larger, which results in a higher future value. This is because the investment grows faster due to the higher rate of return.
3. Consider the effect of a smaller initial amount: A smaller principal (P) would reduce the future value, as the base amount being compounded is smaller. This does not lead to an increase in future value.
4. Evaluate the impact of decreasing the number of compounding periods: Reducing the number of compounding periods (n) would result in less frequent application of interest, which decreases the future value. This does not lead to an increase in future value.
5. Understand the effect of withdrawing funds periodically: Periodic withdrawals reduce the principal amount available for compounding, which decreases the future value. This does not lead to an increase in future value.