Chapter 5 (Interest Rates)
Suppose your bank account pays interest monthly with the interest rate quoted as an effective annual rate (EAR) of 6%. What amount of interest will you earn each month? If you have no money in the bank today, how much will you need to save at the end of each month to accumulate $100,000 in 10 years?
-A 6% EAR is equivalent to earning (1.06)^(1/12) -1 = 0.48668% per month. -We can view this savings plan as a monthly annuity with 10 x 12 = 120 payments. -We can compute this using excel: NPER = 120 Rate = 0.4868% PV = 0 Solve for Pmt FV = 100,000 -Thus, if we save $615.47 per month and we earn interest monthly at an EAR of 6%, we will have $100,000 in 10 years
The Determinants of Interest Rates
-Fundamentally, interest rates are determined in the market based on individuals' willingness to borrow and lend
Nominal Interest Rates
-Indicate the rate at which your money will grow if invested for a certain period.
Effective Annual Rate (EAR)
-Indicates the actual amount of interest that will be earned at the end of one year. -In general, by raising the interest rate factor (1 +r) to the appropriate power, we can compute an equivalent interest rate for a longer time period
Annual Percentage Rate (APR)
-Indicates the amount of simple interest earned in one year, that is, the amount of interest earned without the effect of compounding -APR quote is typically less than the actual amount of interest that you will earn -We cannot use the APR itself as a discount rate. -Divide the APR by the number of compounding periods per year to determine the actual interest rate per compounding period
Real Interest Rate
-The rate of growth of your purchasing power, after adjusting for inflation, is determined by the real interest rate, which we denote by rr. -The real interest rate is approximately equal to the nominal interest rate less the rate of inflation
Growth in Purchasing Power
Growth in Purchasing Power = 1 + real interest rate Growth in Purchasing Power = (Growth of Money) / (Growth of Prices)
You have just graduated and need money to buy a new car. Your rich Uncle Henry will lend you the money so long as you agree to pay him back within four years, and you offer to pay him the rate of interest that he would otherwise get by putting his money in a savings account. Based on your earnings and living expenses, you think you will be able to pay him $5000 in one year, and then $8000 each year for the next three years. If Uncle Henry would otherwise earn 6% per year on his savings, how much can you borrow from him?
Thus, Uncle Henry should be willing to lend you $24,890.65 in exchange for your promised payments. This amount is less than the total you will pay him ($5000+$8000+$8000+$8000($5000+$8000+$8000+$8000=$29,000)=$29,000) due to the time value of money.
You have been offered the following investment opportunity: If you invest $1000 today, you will receive $500 at the end of each of the next three years. If you could otherwise earn 10% per year on your money, should you undertake the investment opportunity?
To decide whether we should accept this opportunity, we compute the NPV by computing the present value of the stream: NPV = -1,000 + (500/1.10) + (500/1.10^2) + (500/1.10^3) = $243.43
