TIME VALUE OF MONEY: Equivalence Is Dependent on Interest Rate.

In the example of Plans 1-4, all calculations were made at an 8% interest rate. At this interest rate, it has been shown that all four plans are equivalent to a present sum of $5000.

But whatwould happen if we were to change the problemby changing the interest rate?

If the interest rate were increased to 9%, we know that the required interest payment for each plan would increase, and the calculated repayment schedules (Table3-1, column f) could no longer repay the $5000 debt with the higher interest. Instead, each plan would repay a sum less than the principal of $5000, because more money would have to be used to repay the higher interest rate. By some calculations, the equivalent present sum that each plan will repay at 9% interest is:

As predicted,at the higher9%interesteachof there payment plans of  Table3-1 repays a present sum less than $5000. But they do not repay the same present sum. Plan 1 would repay $4877 with 9%interest, while Plan 2 would repay $4806.Thus, with interest at 9%, Plans 1 and 2 are no longer equivalent, for they will not repay the same present sum. The two series of payments (Plan 1 and Plan 2) were equivalent at 8%, but not at 9%. This leads to the conclusion that equivalence is dependent on the interest rate. Changing the interest rate destroys the equivalence between two series of payments.

Could we create revised repayment schemes that would be equivalent to $5000 now with interest at 9%? Yes, of course we could: to revise Plan I of Table 3-1, we need to increase the total end-of-year payment in order to pay 9% interest on the outstanding debt.

Plan 2 of Table 3-1 is revised for 9% interest by increasing the first four payments to 9% x $5000 = $450 and the finalpayment to $5450.Twoplans that repay $5000in 5 years with interest at 9% are:

We have determined that Revised Plan 1 is equivalentto apresent sum of  $5000and Revised Plan 2 is equivalentto $5000 now; it follows that at 9% interest, Revised Plan 1 is equivalent to Revised Plan 2.