Final answer:
The future value of a lump-sum investment will increase with a higher interest rate or a larger initial investment amount; however, a longer time period, not a shorter one, is advantageous for compound interest to accumulate. To illustrate, a $3,000 deposit at a 7% interest rate will grow significantly over 40 years.
Step-by-step explanation:
The future value of a lump-sum investment will increase if you do any of the following:
- Increase the interest rate: A higher interest rate will compound more earnings on the original investment.
- Increase the initial investment amount: A larger base amount will increase the amount of money that is accruing interest.
However, decreasing the time period does not increase the future value of the investment. The longer the time period, the more time there is for compound interest to work its magic. To illustrate, an initial deposit of $3,000 at a 7% annual rate of return for 40 years will grow substantially, demonstrating the power of compound interest in long-term investments.
If the interest rate were to increase, for example from 8% to 11%, the present value of the future payments would be lower because they are now being discounted at a higher rate. The same principle applies to the growth of an investment over time with compound interest.