Section 5.1 Introduction to Equations of Value
There are times that a series of debts owed by an individual might have need to be replaced with another set of debts with perhaps different amounts and at perhaps different times. To determine how to set this up in an equitable manner requires an "equation of value". To create an equation of value, draw a time line with debts above and payments below. Choose a date to focus on (often a payment date) and then determine the value of all debts and payments at that time. Finally, set the value of payments = value of debts.
Example 5.1.1.
Consider the situation where one owes a debt of \(\$ 20000\) in 4 years and \(\$ 30000\) in 8 years with money compounded quarterly at a nominal rate of 8%. One might desire to combine these two debts into a single payment of size X, say, on the 6th year. yields the following equation of value:
and arithmetic easily yields
Example 5.1.2.
Consider a situation similar to above but now where one owes the same debts of \(\$ 20000\) in 4 years and \(\$ 30000\) in 8 years with money compounded quarterly at a nominal rate of 8% but with the desire to convert this to two payments each of size X, say, on the 6th year and 7th year. This yields the following equation of value:
and a little but of algebra and arithmetic yields