INTEREST RATES AND BOND PRICES
by
Charles Lamson
Change must be measured from a known baseline.
---Evan Schwiit
The Present Versus the Future
State University currently charges students $5,000 a year for tuition. Following the appointment of an innovative financial officer. it offers enrolling freshmen a new way to pay four years tuition---pay $18,000 today, rather than $5,000 per year for four years. Would you participate in the plan? Following her third box office smash, a Hollywood sensation has just signed a multipicture contract. As Compensation, the star has been offered either $6 million today or $7.5 in five years. You are her financial adviser; what should she do and why? You win a million-dollar lottery and learn that the million dollars will be paid out in equal installments of $50,000 per year, over the next 20 years. Would you be willing to trade this stream of future income for one payment today? How large would that payment have to be?
The Time Value of Money
The interest rate is the cost to borrowers of obtaining credit, and the reward to lending for surplus funds. Thus, just as rent is the cost to apartment dwellers and the return to the landlord, the interest rate is the rental rate paid by borrowers and received by lenders when money is "rented out."
The central point to remember from this discussion, is the role the interest rate plays in linking the present with the future. Lending in the present enables spending in the future the sum of what is lent, plus the interest earned. Borrowing in the present enables spending in the present, but requires paying back in the future, what I borrowed plus interest. Since the interest rate is the return on lending, and the cost, of borrowing; it plays a pivotal role in spending, saving, borrowing, and lending decisions made in the present and bearing on the future. The concept I have been describing is called time value of money. Simply put, the interest rate represents the time value of money, because it specifies the terms upon which one can trade off. present purchasing power for future purchasing power. This is one of the most important and fundamental concepts in economics and finance.
Compounding and Discounting
Compounding: Futures
Compounding is a method used to answer a simple question: What is the future value of money lent or borrowed today? As is illustrated in Exhibit 1. the question is forward looking; we stand in the present today, and ask a question about the future.
1. Compounding: The Future Value of Money Lent Today
Click to enlarge.
Suppose Joseph A. Student agrees to lend a friend $1,000 for one year, the friend gives Joe an IOU for $1,000 and agrees to repay the $1,000 interest in a year. The amount that is originally lent is the principal---in this case $1,000. If the agreed interest rate is 6 percent, then the friend will pay total of $1,060 ($1,00 + $60).
Imagine now that Joe's friend borrows for two years instead of one year and makes no payments to Joe until two years pass. Here, is where compounding comes into play. Literally, compounding means to combine, add to, or increase. In the financial world, it refers to the increase in the value of funds that results from earning interest on interest. More specifically, interest earned after the first year is added to the original principal; the second year's interest calculation is based on this total. The funds to be received at the end of two years.
Discounting: Present Values
Compounding is forward looking. It addresses the question: What is the future value of money lent (or borrowed) today? As we shall see, understanding compounding is of money (lent) or borrowed (or borrowed) today? As we shall see understanding compounding is the key to really understanding what often seems to be a more difficult concept to grasp---discounting.
In effect, as shown in Exhibit 2, discounting is backward looking. It addresses this question: What is the present value of money to be received (or paid) in the future?
2. Discounting the Present Value of Money to Be Received in the Future
Recap
Compounding is finding the future value of a present sum. Discounting is finding the present value of a future sum.
*SOURCE: THE FINANCIAL SYSTEM AND THE ECONOMY, 3RD ED., 2003, MAUREEN BURTON & RAY LOMBRA, PGS. 130-133*
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