FInanCIal Markets 65
Interest rates are a critical economic indicator, frequently reported by the media due to their significant impact on daily life and the overall economy They play a vital role in personal financial decisions, influencing choices about consumption, savings, home purchases, and investment in bonds or savings accounts Additionally, interest rates affect business and household economic strategies, determining whether to invest in new equipment or save funds in a bank.
Before studying money, banking, and financial markets, it's essential to understand the term "interest rates." The yield to maturity serves as the most accurate measure of interest rates, reflecting what economists refer to when discussing this concept We will examine how yield to maturity is measured and highlight that a bond's interest rate does not always indicate its investment quality, as the rate of return may differ from the stated interest rate Additionally, we will differentiate between real interest rates, which account for inflation, and nominal interest rates, which do not.
While learning definitions may not be the most thrilling task, it is crucial to read attentively and comprehend the concepts in this chapter A solid understanding of these terms will not only enhance your grasp of interest rates but also clarify their significance in your life and the broader economy.
Debt instruments generate varying cash flows with distinct timing, necessitating a comparison of their values Understanding how to evaluate different types of debt instruments is essential before exploring interest rate measurements This comparison relies on the concept of present value.
The present value concept highlights that a dollar received in the future holds less value than a dollar in hand today, emphasizing the importance of understanding interest rates.
A dollar received today is more valuable than a dollar received in the future, as depositing it in a savings account that earns interest will yield more than one dollar after a year This concept is supported by economists who provide a formal definition of the time value of money.
A simple loan is a basic type of debt instrument where the lender gives the borrower a principal amount that must be repaid by a specified maturity date, along with interest For instance, if you lend your friend Jane a sum of money, she will need to return the principal plus any agreed-upon interest by the due date.
For a loan of $100 over one year, the borrower must repay the principal amount along with an interest payment, totaling $110 In this case, the interest payment of $10 provides a straightforward way to calculate the simple interest rate, represented as $i = \frac{10}{100}$.
If you make this $100 loan, at the end of the year you would have $110, which can be rewritten as
If you then lent out the $110, at the end of the second year you would have
$100 * 11 + 0.102 * 11 + 0.102 = $100 * 11 + 0.102 2 = $121 Continuing with the loan again, you would have at the end of the third year
$121 * 11 + 0.102 = $100 * 11 + 0.102 3 = $133 Generalizing, we can see that at the end of n years, your $100 would turn into
The amounts you would have at the end of each year by making the $100 loan today can be seen in the following timeline:
This timeline illustrates that receiving $100 today is equivalent in happiness to receiving $110 in one year, provided you trust that Jane will repay you Similarly, having $100 today is just as satisfying as receiving $121 in two years, $133 in three years, or $100 multiplied by 11 plus an additional 0.102 for every year in the future.
The timeline tells us that we can also work backward from future amounts to the pres- ent For example, $133 = $100 * 11 + 0.102 3 three years from now is worth $100 today, so that
The method of determining the present value of future cash flows is known as discounting the future This can be expressed using the formula, where the present value (PV) of $100 is represented alongside a future cash flow (CF) of $133, with the interest rate denoted as \(i\) instead of a fixed value like 0.10 (10%).
Equation 1 illustrates that a promised cash flow of $1 in ten years is less valuable than $1 today, as the present amount could be invested to yield a greater future value The present value concept is essential for determining the current worth of a debt market instrument by summing the present values of all future payments at a specified interest rate \(i\).
This information enables us to compare the values of two or more instruments with very different timing of their payments.
What is the present value of $250 to be paid in two years if the interest rate is 15%?
The present value would be $189.04 Using Equation 1
11 + i2 n where CF = cash flow in two years = $250 i = annual interest rate = 0.15 n = number of years = 2 Thus
ApplicAtion ◆ How Much Is That Jackpot Worth?
Winning a $20 million jackpot in the New York State Lottery sounds thrilling, but it's important to understand that this amount is paid out as $1 million annually over twenty years Therefore, while the total prize is $20 million, the actual immediate cash you receive is significantly less, raising the question of whether you have truly "won" the full amount.
In today's dollars, the $20 million prize is worth significantly less due to the concept of present value Assuming a 10% interest rate, the first payment of $1 million retains its full value, but subsequent payments diminish in worth; for example, the second payment is valued at approximately $909,090, and the third at around $826,446 When all payments are totaled, they amount to only $9.4 million While the initial figure seems exciting, understanding present value reveals that the actual winnings are less than half of the advertised amount.
Four types of Credit Market Instruments
In terms of the timing of their cash flow payments, there are four basic types of credit market instruments.
A simple loan involves a lender providing funds to a borrower, who is required to repay the principal amount along with interest by the maturity date This type of financing is common in money market instruments, such as commercial loans extended to businesses.
A fixed-payment loan, also known as a fully amortized loan, is a type of financing where the lender provides a specific amount of funds to the borrower The borrower is required to repay this amount through consistent payments, typically on a monthly basis, which include both principal and interest over a predetermined period.
$1,000, a fixed-payment loan might require you to pay $126 every year for 25 years Installment loans (such as auto loans) and mortgages are frequently of the fixed- payment type.