We will examine the effect by monitoring four people, two of them are referred to as savers, and two of them are referred to as debtors:
- The bank offers saver A (Jane) a savings plan at 8% annual interest.
- The bank offers saver B (Joe) a savings plan at 6% annual interest.
- The bank charges debtor A (Mike) 15% annual interest.
- The bank charges debtor B (Sandra) 18% annual interest.
When each of these persons calculates the present value of any future sum, for example $1,000 (that he must receive or pay one year from now), he takes into account the interest rate that is relevant for him.
This means that the present value of any future sum ($1,000) will be different for each person, depending on the interest rate that he uses:
The higher the relevant interest rate, the lower the present value.
Comparing the Savers
Saver A (Jane) calculated the present value of $1,000, and found that it was $926 (rounded-off). For saver B (Joe), the present value of the same amount will be $943, which is higher than Jane’s present value for $1,000.
Explanation:
The interest that Jane receives for her savings is higher than the interest that Joe receives. For that reason, Joe needs to deposit a greater amount in order to have $1,000 a year from now, and he will have to deposit a larger amount than Jane.
Summary:
Beginning of the year:
Jane $926 8% End of the year: $1,000.
Beginning of the year:
Joe $943 6% End of the year: $1,000.
Comparing the Debtors
The present value of this future amount will be $870 for Mike and $847 for Sandra (a smaller amount).
