Final answer:
The future value (FV) is larger than the present value (PV) due to the compounding effect of interest rates over time. Interest earned in each period contributes to the growth of the investment, resulting in a higher future value.
Step-by-step explanation:
The future value (FV) is larger than the present value (PV) because of the compounding effect of interest rates over time. When money is invested, it can earn interest, which is added to the initial amount and then earns interest of its own. This compounding effect results in the future value being greater than the present value.
For example, let's say you invest $1,000 at an annual interest rate of 10% for 5 years. After the first year, you would earn $100 in interest, bringing your total to $1,100. In the second year, you earn interest on the full $1,100, resulting in $110 of interest and a new total of $1,210. This process continues, and after 5 years, your initial $1,000 would have grown to $1,610. The interest earned in each period contributes to the growth of the investment, leading to a larger future value than the initial present value.
Interest rate compounding is an essential concept in the Time Value of Money. It allows individuals and businesses to understand the potential growth of their investments over time and make informed financial decisions.