Question

time value of money and term structure of interest rates : how to borrow in the market and how to invest in the market without other risks and only considering the time value of money?

How to borrow in the market and how to invest in the market without get the risks? (just give the explanation)

and the formula for Time value of money and term structure of interest rates.

Answer 1

Money is worth more more in the present than in the future because there's an opportunity cost to waiting for it. In addition to your loss of use if you don't get your hands on it right away, there's also inflation gradually eroding its value and purchasing power.

If you're going to part with your money for any period of time, you probably expect a larger sum returned to you than you started with. Whether you're lending or investing, the goal is to make a gain to compensate you for going without your money for awhile.

Time is also money when it comes to paying off debt.  Whether it is credit card debt, student loan debt, or a mortgage, the more time it takes you to pay the debt, the more money it will cost you.  This is so because of the interest, or finance charge involved in borrowed money.  The longer it takes to pay off a loan, the more interest accrues.   

As individuals, we often face decisions that involve saving money for a future use, or borrowing money for current consumption. We then need to determine the amount we need to invest, if we are saving, or the cost of borrowing, if we are shopping for a loan. As investment analysts, much of our work also involves evaluating transactions with present and future cash flows. When we place a value on any security, for example, we are attempting to determine the worth of a stream of future cash flows. To carry out all the above tasks accurately, we must understand the mathematics of time value of money problems. Money has time value in that individuals value a given amount of money more highly the earlier it is received. Therefore, a smaller amount of money now may be equivalent in value to a larger amount received at a future date. The time value of money as a topic in investment mathematics deals with equivalence relationships between cash flows with different dates. Mastery of time value of money concepts and techniques is essential for investment analysts.

Formula for Calculating the Time Value of Money

So how do you measure the time value of money? The formula takes the present value, then multiplies it by compound interest for each of the payment periods and factors in the time period over which the payments are made.

Formula: FV = PV x [ 1 + (i / n) ] ^(n x t)

• (PV) Present Value = What your money is worth right now.
• (FV) Future Value = What your money will be worth at some future time after it (hopefully) earns interest.
• (I) Interest = Paying someone for the time their money is held.
• (N) Number of Periods = Investment (or loan) period.
• (T) Number of Years = Amount of time money is held
  
  The term structure of interest rates – known as the yield curve – is the relationship between interest rates or bond yields that differ in their length of time to maturity. The term structure reflects investor expectations about future changes in interest rates and their assessment of monetary policy conditions. The term structure of interest rates is constructed by graphing the YTM and respective maturity dates of benchmark fixed-income securities. Because U.S. Treasuries are considered risk-free, their yields are often used as the benchmark.

• The term structure of interest rates is graphed as though each coupon payment of a noncallable fixed-income security were a zero-coupon bond that matured on the coupon payment date. If the normal yield curve changes shapes, it can be a signal to investors that it’s time to update their economic outlook.