**Steps in the Process** **Step 1: Press CF key** **Step 2: Press 2nd CLR Work keys** **Step 3: ***For CF0* Press 0 Enter ↓ keys **Step 4: ***For C01* Press 600 Enter ↓ keys **Step 5: ***For F01* Press 2 Enter ↓ keys **Step 6: ***For C02* Press 400 Enter ↓ keys **Step 7: ***For F02* Press 2 Enter ↓ keys **Steps in the Process** **Steps in the Process** **Step 8: ***For C03* Press 100 Enter ↓ keys **Step 9: ***For F03* Press 1 Enter ↓ keys **Step 10: Press ↓ ↓ keys** **Step 11: Press NPV key** **Step 12: ***For I *=*,* Enter 10 Enter ↓ keys **Step 13: Press CPT key** -
**Result: ***Present Value* = *$1,677.15* **Solving the Mixed Flows Problem using CF Registry** **General Formula:** **General Formula:** **FVn = PV0(1 + [i/m])mn** ** n: Number of Years m: Compounding Periods per Year i: Annual Interest Rate FVn,m: FV at the end of Year n** ** PV0: PV of the Cash Flow today** **Julie Miller has $1,000 to invest for 2 Years at an annual interest rate of 12%.** **Julie Miller has $1,000 to invest for 2 Years at an annual interest rate of 12%.** **Annual FV2 = 1,000(1 + [0.12/1])(1)(2) = 1,254.40** **Semi FV2 = 1,000(1 + [0.12/2])(2)(2) = 1,262.48** **Qrtly FV2 = 1,000(1 + [0.12/4])(4)(2) = 1,266.77** **Qrtly FV2 = 1,000(1 + [0.12/4])(4)(2) = 1,266.77** **Monthly FV2 = 1,000(1 + [0.12/12])(12)(2) = 1,269.73** **Daily FV2 = 1,000(1 + [0.12/365])(365)(2) = 1,271.20** **The result indicates that a $1,000 investment that earns a 12% annual rate compounded quarterly for 2 years will earn a future value of $1,266.77.** **Solving the Frequency Problem (Quarterly)** **Press****:** **Press****:** ** 2nd P/Y 4 ENTER** ** 2nd QUIT** ** 12 I/Y** ** –1000 PV** ** 0 PMT** ** 2 2nd xP/Y N** ** CPT FV** **Solving the Frequency Problem (Quarterly Altern.)** **The result indicates that a $1,000 investment that earns a 12% annual rate compounded daily for 2 years will earn a future value of $1,271.20.** **Solving the Frequency Problem (Daily)** **Press****:** **Press****:** ** 2nd P/Y 365 ENTER** ** 2nd QUIT** ** 12 I/Y** ** –1000 PV** ** 0 PMT** ** 2 2nd xP/Y N** ** CPT FV** **Solving the Frequency Problem (Daily Alternative)** *Source*: Courtesy of Texas Instruments **Effective Annual Interest Rate** **The actual rate of interest earned (paid) after adjusting the ***nominal rate* for factors such as the number of compounding periods per year. -
**(1 + [ i / m ] )m – 1** **Effective Annual Interest Rate** **Basket Wonders (BW) ****has a $1,000 CD at the bank. The interest rate is 6% compounded quarterly for 1 year. What is the Effective Annual Interest Rate (EAR)?** **Basket Wonders (BW) ****has a $1,000 CD at the bank. The interest rate is 6% compounded quarterly for 1 year. What is the Effective Annual Interest Rate (EAR)?** ** EAR = ( 1 + 0.06 / 4 )4 – 1 = 1.0614 - 1 = 0.0614 or 6.14%!** **BWs Effective Annual Interest Rate** **Press****:** **Press****:** ** 2nd I Conv** ** 6 ENTER** ** ↓ ↓** ** 4 ENTER** ** ↑ CPT** ** 2nd QUIT** *Source*: Courtesy of Texas Instruments **1. Calculate the payment per period.** **1. Calculate the payment per period.** **2. Determine the interest in Period t. ***(Loan Balance at t – 1) x (i% / m)* **3. Compute principal payment in Period t. ***(Payment - Interest from Step 2)* **4. Determine ending balance in Period t. ***(Balance - principal payment from Step 3)* **5. Start again at Step 2 and repeat.** **Julie Miller is borrowing $10,000 at a compound annual interest rate of 12%. Amortize the loan if annual payments are made for 5 years.** **Julie Miller is borrowing $10,000 at a compound annual interest rate of 12%. Amortize the loan if annual payments are made for 5 years.** **Step 1: Payment** ** PV0 = R (PVIFA i%,n)** ** $10,000 = R (PVIFA 12%,5)** ** $10,000 = R (3.605)** ** R = $10,000 / 3.605 = $2,774** **Amortizing a Loan Example** - [Last Payment Slightly Higher Due to Rounding]
**Amortizing a Loan Example** **The result indicates that a $10,000 loan that costs 12% annually for 5 years and will be completely paid off at that time will require $2,774.10 annual payments.** **Press****:** **Press****:** ** 2nd Amort** ** 1 ENTER** ** 1 ENTER** **Results****:** **BAL = 8,425.90* ↓** **PRN = –1,574.10* ↓** **INT = –1,200.00* ↓** *Source*: Courtesy of Texas Instruments **Press****:** **Press****:** ** 2nd Amort** ** 2 ENTER** ** 2 ENTER** **Results****:** **BAL = 6,662.91* ↓** **PRN = –1,763.99* ↓** **INT = –1,011.11* ↓** **Using the Amortization Functions of the Calculator** *Source*: Courtesy of Texas Instruments **Press****:** **Press****:** ** 2nd Amort** ** 1 ENTER** ** 5 ENTER** **Results****:** **BAL = 0.00 ↓** **PRN = – 10,000.00 ↓** **INT = –3,870.49 ↓** **Entire 5 Years of loan information** **(see the total line of 3-82)** **Using the Amortization Functions of the Calculator** *Source*: Courtesy of Texas Instruments **2. Calculate Debt Outstanding – The quantity of outstanding debt may be used in financing the day-to-day activities of the firm.** **2. Calculate Debt Outstanding – The quantity of outstanding debt may be used in financing the day-to-day activities of the firm.** **1. Determine Interest Expense – Interest expenses may reduce taxable income of the firm.** **Usefulness of Amortization**
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