Final answer:
The time value of money indicates that for a positive interest rate, the future value is typically larger than the present value because money can earn interest over time. The present value represents what future money is worth today. Market interest rate fluctuations affect the value of investments like bonds.
Step-by-step explanation:
When explaining the time value of money factors to your friend, it's important to understand that the future value will typically be larger than the present value if there is a positive interest rate. This is because money has the potential to grow over time due to earning interest or returns on investment. Given a 15% interest rate, the future value of an investment will increase with each compounding period.
For example, let's say we want to find the future value of $20 million received in one year. Using the formula:
Future value = Present value × (1 + Interest rate)Number of periods
Assuming an annual compounding, the calculation for the future value after one year at a 15% interest rate would be:
Future value = $20 million × (1 + 0.15)1 = $23 million
This demonstrates the growth due to the interest rate over a single period. Additionally, if the number of periods increases, the future value will grow even more, highlighting the effect of compound interest.
On the other hand, present value calculations aim to determine what an amount of money in the future is worth today. This is useful to know how much you should be willing to pay now for future payments. For instance, if you're expecting to receive $125 in one year and the interest rate is 25%, the present value would be $100.
Moreover, an understanding of interest rate risk is necessary when investing in instruments like bonds. If market interest rates rise, the present value of future payments from existing bonds will decrease because new bonds are more attractive. Thus, the investment's market value will likely fall.