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Chapter 4 - Future value, present value, and interest rates. After studying this chapter you will be able to understand: The value of a payment depends on when it is made, present value can be used to value any stream of future payments, the real interest rate is the nominal interest rate minus expected inflation. It expresses the interest rate in terms of purchasing power rather than current dollars. | Chapter Four 4- A Brief History of Lending Lenders have been despised throughout history. Credit is so basic that we find evidence of loans going back five thousand years. It is hard to imagine an economy without it. Yet, people still take a dim view of lenders because they charge interest. 4- Introduction Credit is one of the critical mechanisms we have for allocating resources. Although interest has historically been unpopular, this comes from the failure to appreciate the opportunity cost of lending. Interest rates Link the present to the future. Tell the future reward for lending today. Tell the cost of borrowing now and repaying later. 4- Valuing Monetary Payments Now and in the Future We must learn how to calculate and compare rates on different financial instruments. We need a set of tools: Future value Present value How and why is the promise to make a payment on one date more or less valuable than the promise to make it on a different date? 4- | Chapter Four 4- A Brief History of Lending Lenders have been despised throughout history. Credit is so basic that we find evidence of loans going back five thousand years. It is hard to imagine an economy without it. Yet, people still take a dim view of lenders because they charge interest. 4- Introduction Credit is one of the critical mechanisms we have for allocating resources. Although interest has historically been unpopular, this comes from the failure to appreciate the opportunity cost of lending. Interest rates Link the present to the future. Tell the future reward for lending today. Tell the cost of borrowing now and repaying later. 4- Valuing Monetary Payments Now and in the Future We must learn how to calculate and compare rates on different financial instruments. We need a set of tools: Future value Present value How and why is the promise to make a payment on one date more or less valuable than the promise to make it on a different date? 4- Future Value and Compound Interest Future value is the value on some future date of an investment made today. $100 invested today at 5% interest gives $105 in a year. So the future value of $100 today at 5% interest is $105 one year from now. The $100 yields $5, which is why interest rates are sometimes called a yield. This is the same as a simple loan of $100 for a year at 5% interest. 4- Future Value and Compound Interest If the present value is $100 and the interest rate is 5%, then the future value one year from now is: $100 + $100(0.05) = $105 This also shows that the higher the interest rate, the higher the future value. In general: FV = PV + PV(i) = PV(1 + i) 4- Future Value and Compound Interest The higher the interest rate or the higher the amount invested, the higher the future value. Most financial instruments are not this simple, so what happens when time to repayment varies. When using one-year interest rates to compute the value repaid more than one year .
