Kinh tế học - Chapter 10: Simple interest

Chapter 10Simple InterestCalculate simple interest and maturity value for months and yearsCalculate simple interest and maturity value by (a) exact interest and (b) ordinary interestSimple Interest#10Learning Unit ObjectivesCalculation of Simple Interest and Maturity ValueLU10.1Using the interest formula, calculate the unknown when the other two (principal, rate, or time) are givenSimple Interest#10Learning Unit ObjectivesFinding Unknown in Simple Interest FormulaLU10.2List the steps to complete the U.S. RuleComplete the proper interest credits under the U.S. RuleSimple Interest#10Learning Unit ObjectivesU.S. Rule -- Making Partial Note Payments before Due DateLU10.3Maturity ValueMaturity Value (MV) = Principal (P) + Interest (I)The amount of the loan(Face value)Cost of borrowingmoneySimple Interest FormulaSimple Interest (I) = Principal (P) x Rate (R) x Time (T)Stated as aPercentStated in yearsJan Carley borrowed $30,000 for office furniture. The loan was for 6 months at an annual interest rate of 8%. What are Jan’s interest and maturity value?SI = $30,000 x.08 x 6 = $1,200 12MV = $30,000 + $1,200 = $31,200Simple Interest FormulaSimple Interest (I) = Principal (P) x Rate (R) x Time (T)Stated as aPercentStated in yearsJan borrowed $30,000. The loan was for 1 year at a rate of 8%. What is interest and maturity value?SI = $30,000 x.08 x 1 = $2,400MV = $30,000 + $2,400 = $32,400Two Methods of Calculating Simple Interest and Maturity ValueExact Interest (365 Days)Time = Exact number of days 365Method 1 – Exact InterestUsed by Federal Reserve banksand the federal governmentI = P X R X T$40,000 x .08 x 124 365$1,087.12MV = P + I$40,000 + $1,087.12$41,087.12Exact Interest (365 Days)On March 4, Peg Carry borrowed $40,000 at 8%. Interest and principal are due on July 6.Two Methods of Calculating Simple Interest and Maturity ValueOrdinary Interest (360 Days)Bankers RuleTime = Exact number of days 360I = P X R X T$40,000 x .08 x 124 360$1,102.22MV = P + I$40,000 + $1102.22$41,102.22Ordinary Interest (360 Days)On March 4, Peg Carry borrowed $40,000 at 8%. Interest and principal are due on July 6.Method 2 – Ordinary InterestBankers RuleTwo Methods of Calculating Simple Interest and Maturity ValueExact Interest (365 Days)I = P X R X T$15,000 x .08 x 98 365$322.19MV = P + I$15,000 + $322.19$15,322.19Ordinary Interest (360 Days)On May 4, Dawn Kristal borrowed $15,000 at 8%. Interest and principal are due on August 10.I = P X R X T$15,000 x .08 x 98 360$326.67MV = P + I$15,000 + $326.67$15,326.67Finding Unknown in Simple Interest Formula - PRINCIPALPrincipal = Interest Rate x TimeTim Jarvis paid the bank $19.48 interest at 9.5% for 90 days. How much did Timborrow using ordinary interest method? $19.48 .P = .095 x (90/360) = $820.21.095 times 90 divided by 360. Do not round answerInterest (I) = Principal (P) x Rate (R) x Time (T)Check: 19.48 = 820.21 x .095 x 90/360Finding Unknown in Simple Interest Formula - RATEInterest (I) = Principal (P) x Rate (R) x Time (T)Check: 19.48 = 820.21 x .095 x 90/360Rate = Interest Principal x TimeTim Jarvis borrowed $820.21 from a bank. Tim’s interest is $19.48 for 90 days. What rate of interest did Tim pay using ordinary interest method? $19.48 .R = $820.21 x (90/360) = 9.5%Finding Unknown in Simple Interest Formula - TIMEInterest (I) = Principal (P) x Rate (R) x Time (T)Check: 19.48 = 820.21 x .095 x 90/360Time (yrs) = Interest Principle x RateTim Jarvis borrowed $820.21 from a bank. Tim’s interest is $19.48 for 90 days. What rate of interest did Tim pay using ordinary interest method? $19.48 .T = $820.21 x .095 = .25 .25 x 360 = 90 daysConvert years to days (assume 360 days)U.S. Rule - Making Partial Note Payments before Due DateAny partial loan payment first covers any interest that has built up. The remainder of the partial payment reduces the loan principal.Allows the borrower to receive proper interest creditsU.S. Rule - ExampleStep 1. Calculate interest on principal from date of loan to date of first principal paymentStep 2. Apply partial payment to interest due. Subtract remainder of payment from principalJoe Mill owes $5,000 on an 11%, 90-day note. On day 50, Joe pays $600 on the note. On day 80, Joe makes an $800 additional payment. Assume a 360-day year. What is Joe’s adjusted balance after day 50 and after day 80? What is the ending balance due?$5,000 x .11 x 50 = $76.39 360$600 - 76.39 = $523.61$5,000 – 523.61 = $4,476.39U.S. Rule - ExampleStep 3. Calculate interest on adjusted balance that starts from previous payment date and goes to new payment date. Then apply Step 2.Step 4. At maturity, calculate interest from last partial payment. Add this interest to adjusted balance.Joe Mill owes $5,000 on an 11%, 90-day note. On day 50, Joe pays $600 on the note. On day 80, Joe makes an $800 additional payment. Assume a 360-day year. What is Joe’s adjusted balance after day 50 and after day 80? What is the ending balance due?$4,476.39 x .11 x 30 = $41.03 360$800 - 41.03 = $758.97$4,476.39 – 758.97 = $3717.42$3,717.42 x .11 x 10 = $11.36 360$3,717.42 + $11.36 = $3,728.78