Chapter 5 Interest Rates 2024 - Finance 235 PDF

235 (2024)  Learning outcomes Chapter 5 Interest Rate Discuss how interest rates are PART 1 quoted. Compute the annual and Periodic Interest rate. Compute the effective annual rate (EAR) on...

235 (2024)  Learning outcomes Chapter 5 Interest Rate Discuss how interest rates are PART 1 quoted. Compute the annual and Periodic Interest rate. Compute the effective annual rate (EAR) on a loan or investment. Explain the real rate of interest and the impact of inflation on nominal rates. Explain Risk Free Rate. Interest Rate It is basically the cost of borrowing money. Interest rates fluctuate over time. Interest rate is a key tool for finance managers. https://www.youtube.com/watch? v=lBYt8Axmt8I Types of Interest Rate Simple Interest Rate & Compound Interest Rate. Annual Percentage rate & Effective Annual rate. Nominal and Real Interest Rates Simple Interest Rate When interest is computed only on the original principal, year after year, the interest is said to be a simple interest. Simple Interest Rate = PRT P= Principal, R= Rate, T= Time Example: If we deposit $100 for 5 years earning simple interest of 10%annually then: $100 x 0.10 x 5 = $50 Compound Interest Rate When the interest is computed for each period and then added to the original principal and earns interest in subsequent periods. Interest earned on interest. Compound Interest Rate = P (1+R)m Example: If we deposit $100 for 5 years earning compound interest of 10%annually then: = [$100 x (1+0.1)5 ]- $100 = £61.05 Comparison How Financial Institutions Quote Interest Rates: Annual and Periodic Interest Rates Certificate of Deposit (CD) at 5% with Bank Quoted rate 5% Annually Annual Percentage Rate (APR): Yearly percentage rate that you earn by investing or charge for borrowing. Most common rate quoted is the annual percentage rate (APR) https://www.youtube.com/watch? v=W9IW58koYJs How Financial Institutions Quote Interest Rates: Annual and Periodic Interest Rates Lenders (Financial institutions) often charge interest on a non-annual basis. E.g., Semi-annually, Quarterly, Monthly, Daily Compounding Period Per Year Frequency of times at which these institutions add interest to an account each year. If investment compounds more times in a year, then we must convert APR into Periodic interest rate. Periodic Interest Rate (C/Y or “m”) Periodic Interest Rate, r = APR/m How Financial Institutions Quote Interest Rates: Annual and Periodic Interest Rates Periodic Interest Rate is calculated by dividing the APR with the number of compounding periods per year (C/Y or “m”). For quarterly compounding then m=4 For Daily Compounding then m = 365 For example: If APR = 12% m = 12 Solution: i % = 12% / 12 = 1% How Financial Institutions Quote Interest Rates: Annual and Periodic Interest Rates Example The First Common Bank has advertised one of its loan offerings as follows: We will lend you $100,000 for up to 3 years at an APR of 10% with interest compounded ____________. FV = 100,000 (1+.10)^3 = $133,100 FV = 100,000 (1+.10/4)^3*4 = $134,488 FV = 100,000 (1+.10/12)^3*12 = $134,818 Example If we Invest $500 with annual compounding of 5% then after one year we will receive $25. But if we Invest the same amount using periodic interest rate then: Date Beginning Interest Earned Ending Bal. Balance 1/1 – 3/31 500 500 x 0.0125 $506.25 = $6.25 4/1 – 6/30 506.25 506.25 x 0.0125 $512.58 = $6.33 7/1 – 9/30 512.58 512.58 x 0.0125 $518.99 = $6.41 10/1 – 12/31 518.99 518.99 x 0.0125 $525.47 = $6.48  Periodic Compounding = 525.47 – 500 = 25.47 Effective Annual Effective Annual Rate = 25.47 / 500 = 5.094 Rate (EAR) Effective Annual Rate (EAR) The EAR is the true rate of return to the lender and true cost of borrowing to the borrower.  EAR depends on the number of compounding periods. EAR, also known as the Annual Percentage Yield (APY) on an investment, is calculated from a given APR and frequency of Effective Annual compounding (m) by using the following Rate (EAR) equation: m   APR  EAR  1   1  m  EAR = (1+ Periodic Interest rate)m -1 Where as: m = number of compounding periods per year Example: (Calculating EAR or APY) The First Women Bank has advertised one of its loan offerings as follows: “We will lend you $100,000 for up to 3 years at an APR of 8.5% with interest compounded monthly.” If you borrow $100,000 for 1 year, how much interest expense will you have accumulated over the first year and what is the bank’s APY? Note: you make no payments during the year and the interest accumulates over the year. Example: (Calculating EAR or APY) Annual Percentage Rate = 8.5% Compounding Period (m)= 12 As we Know: Periodic interest rate = APR/m = 8.5%/12 = 0.70833% =.0070833 APY or EAR = (1 + 0.0070833)12 - 1 = 1.0883909 - 1 = 8.83909% Total interest expense after 1 year =.0883909 x $100,000 = $8,839.09 Nominal and Real Interest Rates Nominal Interest Rate: Rate at which money invested grows. e.g., interest earned on an investment Nominal rate = Real rate + expected Inflation Real Interest Rate: Rate at which the purchasing power of an investment increases. Real rate = Nominal rate - expected Inflation Inflation: Rate at which prices as a whole are increasing. Risk Free Rate Theoretical interest rate at which an investor is guaranteed to earn the subscribed rate and at which the borrower will never default. Very clean customers Reliable securities Safe investment Default Premium The portion of interest rate that is compensated for the higher risk associated and the probability that a borrower will default. Chance of default Unsafe investment Maturity Premium It is the portion of nominal interest rate that compensates the investor for the additional waiting time or the lender for the additional time to take to receive repayment in full. Yield Curve It shows the relationship of the Downward-sloping yield curve interest rate to the maturity date of a particular financial instrument. Upward-sloping yield curve