Interest Rate

Any entity borrowing money from a lender, also need to pay a cost, known as the interest. Till the entire principal is repaid back to the lender, the borrower has to pay this interest, that in most cases is in the form of periodic payments to the lender.

In finance, the term interest rate refers to this cost (or interest) expressed as a percentage of the principal amount.

In any society, there is no dearth for borrowers or lenders, and therefore, the different types of interest rates from the Fed fund rates to the rate charged by a loan shark.

Let's take a look at a few important borrowers in the US economy.

1. US Government, where the Govt pays an interest to those investors purchasing its Treasury notes and bonds.

2. A Savings Bank, where the Bank will give an interest on the saving deposits.

3. An individual taking a mortgage loan, making the monthly payments at an interest rate charged by the lender.

4. A depository institution (such as a Bank) borrowing money from another depository institution to meet the reserve requirements. The interest rate in this case is fixed by the Federal Reserve and is known as the Fed Funds rate.

5. A corporation issuing a bond.

Normally, all these interest rates move together, that, when we talk about increasing interest rates in an economy, it refers to the general trend of increasing borrowing costs for the Treasury or a home buyer.

How are these interest rates moving in tandem ?

Size of Bond Markets

To give a perspective on the size of Bond Markets.

Data from 2008 (SIFMA report)

Total outstanding debt in US Bond Market is $ 33 trillion. We'll break this into the following sectors -

1. Mortgage - 26.57 %
2. Corporate - 18.52 %
3. Treasury - 18.16 %
4. Money M - 11.32 %
5. Agency - 9.58 %
6. Asset - 7.98 %
7. Muncipal - 7.87 %

As of 2008, Mortgage backed bonds constitute the biggest sector in the US Bond market, followed by the bonds issued by companies (corporate sector).

The size of the Treasury sector in 2008 was 18.16 %, or 6.08 trillion. The total US debt for the same year was 9.99 trillion. So, Treasury bonds constitute most of the US Govt's debt.

A Comparison of various borrowers -

US Govt - 9985 billion (Including 6082 billion treasury debt)
Japan Govt - 9294 billion
India Govt - 1989 billion
Russia Govt - 141 billion (One of the lowest)
GM - 28 billion (When it filed for Bankruptcy in 2009)

Reference - http://www.sifma.org/uploadedFiles/Research/Statistics/SIFMA_USBondMarketOutstanding.pdf

Time Value of Money

This is to start a series of tutorials, with the aim to help the reader build a strong understanding of the complex financial world. To start, let's try to understand the time value concept of money.

Prerequisites :

Concept of compounding

Given two examples of future income, how can one tell, which of the two is better ?

Say, you won a lottery, but given the choice of,

Option A : Receiving $ 100 after 2 years
or
Option B : Receiving $ 110 after 4 years

We also have following assumptions -

1. There is no risk of whether or not you will receive the amount.
2. No inflation for the given time period.

Given that, your task is to choose the better option. Let's see.

Suppose you have a Bank that gives an interest rate of 1 % per annum. We'll compute, how much invested today, would fetch you $ 100 after 2 years, and $ 110 after 4 years [For the formula, see Concept of compounding].

For option A : 100 / (1.01) ** 2 = $ 98.03

For option B : 110 / (1.01) ** 4 = $ 105.70

As you can see, if you choose option B (i.e., receiving $ 110 after 4 years), it's equivalent to having 105.70 dollars in your hand today, and is definitely better than having $ 98.03 (Option A).

Now, instead of 1 %, what if the interest rate in your bank is 10 % per annum. Let's again compute how much each of these are worth today.

Option A : 100 / (1.1) ** 2 = $ 82.64

Option B : 110 / (1.1) ** 4 = $ 75.13

Definitely, option A is better in such a scenario.

There are two relations that we need understand from this small example and which are extremely important in the study of finance.

1. If the prevailing interest rates are high, it means a future cash flow is less significant today. And the vice versa, that if the prevailing interest rates are low, a future cash flow can be much more significant.

Take option A alone, and note how the present value of the investment diminished when the interest rates rose from 1 % to 10 %. Same is the case with option B.

Mathematically, this is the same inverse relation of Present value and discount rate.

2. A cash flow from the far future is more sensitive to interest rates than a cash flow from the near future.

In the above example, as a result of interest rate change from 1% to 10%, the value of the cash flow after 4 years (Option B), diminished much more than it did for the 2 years option.

This relation is due to the multiplication effect of the time factor in the Present Value formula.

Most of the real world financial instruments, such as bonds, mortgage loans and insurance have to do with a series of such future cash flows. In the next section, we'll cover the Net Present Value of a series of future cash flows.