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I have a question how does the value of i (interest rate) is 0.075 in the example eventhough it said 9.5% p.a. Is there any calculation involved in geting that 0.075 from 9.5%. Enlighten me if I'm wrong. Thank You.

I have a question how does the value of i (interest rate) is 0.075 in the example eventhough it said 9.5% p.a. Is there any calculation involved in geting that 0.075 from 9.5%. Enlighten me if I'm wrong. Thank You.

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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Hello. I have a question how does the value of i (interest rate) is 0.075 in the example eventhough it said 9.5% p.a. Is there any calculation involved in geting that 0.075 from 9.5%. Enlighten me if I'm wrong. Thank You.

Conversion P to F F to P A to F F to A P to A Table 9.1. Commonly Used Factors for Cash Flow Diagram Calculations Symbol Common Name Eq. No. (F/P, i, n) (9.5) A to P (P/F, i, n) (F/A, i, n) (A/F, i, n) (A/P, i, n) (P/A, i, n) Single Payment Compound Amount Factor Single Payment Present Worth Factor Uniform Series Compound Amount Factor, Future Worth of Annuity Sinking Fund Factor Capital Recovery Factor Uniform Series Present Worth Factor, Present Worth of Annuity (9.6) (9.11) (9.12) (9.13) (9.14) Formula (1 + i)" 1 (1 + i)" (1 + i)" - 1 (1 + i)" - 1 i(1 + i)" (1 + i)" - 1 (1 + i)" - 1 i(1 + i)"
Transcribed Image Text:Conversion P to F F to P A to F F to A P to A Table 9.1. Commonly Used Factors for Cash Flow Diagram Calculations Symbol Common Name Eq. No. (F/P, i, n) (9.5) A to P (P/F, i, n) (F/A, i, n) (A/F, i, n) (A/P, i, n) (P/A, i, n) Single Payment Compound Amount Factor Single Payment Present Worth Factor Uniform Series Compound Amount Factor, Future Worth of Annuity Sinking Fund Factor Capital Recovery Factor Uniform Series Present Worth Factor, Present Worth of Annuity (9.6) (9.11) (9.12) (9.13) (9.14) Formula (1 + i)" 1 (1 + i)" (1 + i)" - 1 (1 + i)" - 1 i(1 + i)" (1 + i)" - 1 (1 + i)" - 1 i(1 + i)"
Example 9.14. You have just won $2,000,000 in the Texas Lottery as one of seven winners splitting up a jackpot of $14,000,000. It has been announced that each winner will receive $100,000/year for the next 20 years. What is the equivalent present value of your winnings if you have a secure investment opportunity providing 9.5% p.a.? From Table 9.1, Equation (9.14), for n = 20 and i = 0.075, P= ($100,000)[(1 + 0.075)20 - 11/[(0.075)(1+0.075) 2⁰1 P= $1,019,000 A present value of $1,019,000 is equivalent to a 20-year annuity of $100,000/y when the effective interest rate is 9.5%.
Transcribed Image Text:Example 9.14. You have just won $2,000,000 in the Texas Lottery as one of seven winners splitting up a jackpot of $14,000,000. It has been announced that each winner will receive $100,000/year for the next 20 years. What is the equivalent present value of your winnings if you have a secure investment opportunity providing 9.5% p.a.? From Table 9.1, Equation (9.14), for n = 20 and i = 0.075, P= ($100,000)[(1 + 0.075)20 - 11/[(0.075)(1+0.075) 2⁰1 P= $1,019,000 A present value of $1,019,000 is equivalent to a 20-year annuity of $100,000/y when the effective interest rate is 9.5%.
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