To solve this problem, we use the present value formula:

PV0=FVn(1+r)n

• PV0PV0is the present value (what we're calculating),
• FVnFVnis the future value ($5,000),
• rris the discount rate (2% or 0.02),
• nn is the number of years (6)

First, plug the values into the formula. Next, calculate1.0261.026, which equals approximately 1.12616. Then, find the reciprocal of 1.12616, which is 0.88957. Now, multiply $5,000 by this value:

So, the present value is approximately$4,447.85. This means that $5,000 in 6 years is worth about $4,447.85 today when using a 2% discount rate. The discount rate reduces the value of future money, showing that money today is more valuable than money received later.

If the discount rate were higher, the present value would be lower, because a higher rate reduces the future amount's value more. If the time period was shorter, the present value would be higher, as there's less time for the value to decrease.

A challenging part of this problem was understanding how the discount rate affects the present value, especially since small changes in the rate can have a noticeable impact over time.

One question I have is: How do you decide what discount rate to use when inflation and interest rates are unpredictable?