Ch.11_Solution_Manual_Ed.1_v7_

Ch.11_Solution_Manual_Ed.1_v7_ - Exercises 11.1 Identify...

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Exercises 11.1 Identify the type of annuity, deferred period, annuity period, and number of payments for the investment and payments in Problems 1 and 2: Exercise 11.1, Solution 1: a. $500 is deposited in a savings account at the end of each month for 3 years but the first deposit is made 5 months from now The payments form an ordinary deferred annuity and the annuity period is 3 years. Payments are made at the end of each payment period (monthly). Therefore, n = 36. Payments start 5 months from now. Therefore, the ordinary annuity term starts 4 months from now (one payment interval before the first periodic payment). Therefore, the deferred period is 4 months. b. $500 is deposited in a savings account at the beginning of every 6 months for 5 years and 6 months and the first deposit is made in 2 years The payments form a deferred annuity due and the annuity period is 5 years and 6 months Payments are made at the beginning of each payment period (semi-annually). Therefore, n = 2 × 5 + 1 = 11. Payments start 2 years from now. Therefore, the term for the annuity due starts at the same time. Therefore, the deferred period is 2 years. Exercise 11.1, Solution 3: This is an ordinary simple deferred annuity as: Payments are made at the end of each payment period (quarterly) Compounding period (quarterly) = payment period (quarterly) The deferred period is 1 year and 9 months. n = 4 payments/year × 5 years = 20 quarterly payments. j = 12% = 0.12, m = 4 = 0.03 quarterly. Step 1: Calculate the present value of the annuity ( PV annuity ) = $148,774.7486… N I/Y P/Y C/Y PV PMT FV 20 12 4 4 ? 10,000 0 From the calculator computations shown, we get the PV = 148,774.7486
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Step 2: Calculate the present value of this amount at the beginning of the deferred period ( PV def ) Deferred period n = m × t = 4 × (1 year and 9 months) = 4 × 1.75 = 7 quarterly periods PV def = PV annuity (1 + i ) - n = 148,774.7486…(1 + 0.03) - 7 = $120,967.4852… = $120,967.49. N I/Y P/Y C/Y PV PMT FV 7 12 4 4 ? 0 148,774.748 6... From the calculator computations shown, we get the PV = -120,967.4852. Therefore, the business would have to invest an amount of $120,967.49.in the high-growth fund. Exercise 11.1, Solution 5: This is an ordinary general deferred annuity as: Payments are made at the end of each payment period (monthly) Compounding period (quarterly) ≠ payment period (monthly) The deferred period is 6 years and 11 months. n = 12 payments/year × 10 years = 120 monthly payments. j = 8% = 0.08, m = 4 = 0.02 quarterly. i 2 = (1 + i ) c – 1 = (1 + 0.02) (4/12) – 1 = 0.006622…monthly. Step 1: Calculate the present value of the annuity ( PV annuity ) = 3000 = $247,833.4192… N I/Y P/Y C/Y PV PMT FV 120 8 12 4 ? 3000 0 From the calculator computations shown, we get the PV = 247,833.4192 Step 2: Calculate the present value of this amount at the beginning of the deferred period ( PV def ) Deferred period n = m × t = 12 × (6 year and 11 months) = 12 × 6.916666.
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Ch.11_Solution_Manual_Ed.1_v7_ - Exercises 11.1 Identify...

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