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CHAPTER THREE THE INTEREST RATE FACTOR IN FINANCING

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Chapter Objectives Present value of a single sum Future value of a single sum Present value of an annuity Future value of an annuity Calculate the effective annual yield for a series of cash flows Define what is meant by the internal rate of return

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Compound Interest PV= present value i=interest rate, discount rate, rate of return I=dollar amount of interest earned FV= future values Other terms: –Compounding –Discounting

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Compound Interest FV=PV (1 + i) n When using a financial calculator: –n= number of periods –i= interest rate –PV= present value or deposit –PMT= payment –FV= future value –n, i, and PMT must correspond to the same period: –Monthly, quarterly, semi annual or yearly.

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The Financial Calculator n= number of periods i=interest rate PV= present value, deposit, or mortgage amount PMT= payment FV= future value When using the financial calculator three variables must be present in order to compute the fourth unknown. –PV or PMT must be entered as a negative

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Future Value of a Lump Sum FV=PV(1+i) n This formula demonstrates the principle of compounding, or interest on interest if we know: –1. An initial deposit –2. An interest rate –3. Time period –We can compute the values at some specified time period.

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Present Value of a Future Sum PV=FV 1/(1+i) n The discounting process is the opposite of compounding The same rules must be applied when discounting –n, i and PMT must correspond to the same period Monthly, quarterly, semi-annually, and annually

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Future Value of an Annuity FVA=P(1+i) n-1 +P(1+i) n-2 ….. + P Ordinary annuity (end of period) Annuity due (begin of period)

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Present Value of an Annuity PVA= R 1/(1+i) 1 + R 1/(1+i) 2 ….. R 1/(1+i) n

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Future Value of a Single Lump Sum Example: assume Astute investor invests $1,000 today which pays 10 percent, compounded annually. What is the expected future value of that deposit in five years? Solution= $1,610.51

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Future Value of an Annuity Example: assume Astute investor invests $1,000 at the end of each year in an investment which pays 10 percent, compounded annually. What is the expected future value of that investment in five years? Solution= $6,105.10

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Annuities Ordinary Annuity –(e.g., mortgage payment) Annuity Due –(e.g., a monthly rental payment)

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Sinking Fund Payment Example: assume Astute investor wants to accumulate $6,105.10 in five years. Assume Ms. Investor can earn 10 percent, compounded annually. How much must be invested each year to obtain the goal? Solution= $1,000.00

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Present Value of a Single Lump Sum Example: assume Astute investor has an opportunity that provides $1,610.51 at the end of five years. If Ms. Investor requires a 10 percent annual return, how much can astute pay today for this future sum? Solution= $1,000

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Payment to Amortize Mortgage Loan Example: assume Astute investor would like a mortgage loan of $100,000 at 10 percent annual interest, paid monthly, amortized over 30 years. What is the required monthly payment of principal and interest? Solution= $877.57

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Remaining Loan Balance Calculation Example: determine the remaining balance of a mortgage loan of $100,000 at 10 percent annual interest, paid monthly, amortized over 30 years at the end of year four. –The balance is the PV of the remaining payments discounted at the contract interest rate. Solution= $97,402.22

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Quantitative Finance Unit 1 Financial Mathematics.

Quantitative Finance Unit 1 Financial Mathematics.

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