Review_Exercises_11.docx - Review Exercises 11 Review Exercise 11 Solution 1 This is an ordinary simple deferred annuity as Payments are made at the end

Review_Exercises_11.docx - Review Exercises 11 Review...

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Review Exercises 11 Review Exercise 11, Solution 1: 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 4 years. n = 4 payments/year × 7 years = 28 quarterly payments. j = 6% = 0.06, m = 4 i = j m = 0.06 4 = 0.015 quarterly. Step 1: Calculate the present value of the annuity ( PV annuity ) PV annuity = PMT [ 1 −( 1 + i ) n i ] = 50,000 [ 1 −( 1 + 0.015 ) 28 0.015 ] = $1,136,335.835… N I/Y P/Y C/Y PV PMT FV 28 6 4 4 ? ¿ 5 0,000 0 From the calculator computations shown, we get the PV = 1,136,335.835 Step 2: Calculate the present value of this amount at the beginning of the deferred period ( PV def ) Deferred period n = 4 years = 4 × 4 = 16 quarterly periods. PV def = PV annuity (1 + i ) _ n = $1,136,335.835… (1 + 0.015) 16 = $895,467.9095… = $895,467.91. N I/Y P/Y C/Y PV PMT FV 16 6 4 4 ? 0 1,136,355.835. .. From the calculator computations shown, we get the PV = 895,467.9095 Therefore, the vegetable oil business would have to invest $895,467.91 in the high-growth fund. Review Exercise 11, Solution 3: This is a general deferred annuity due as: Payments are made at the beginning of each payment period (quarterly) Compounding period (semi-annually) ≠ payment period (quarterly) The deferred period is 2 years. n = 4 payments/year × 8 years = 32 quarterly payments. j = 7.5% = 0.075, m = 2 Last updated: July 28, 2014
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i = j m = 0.075 2 = 0.0375 semi-annually. c = Number of compounding periods per year Number of payments per year = 2 4 i 2 = (1 + i ) c – 1 = (1 + 0.0375) (2/4) – 1 = 0.018577… quarterly. Step 1: Calculate the present value of the annuity ( PV Due ) ) (1 ) (1 1 2 i 2 i 2 i n PMT Due PV = 800 [ 1 −( 1 + 0.018577 ... ) 32 0.018577... ] ( 1 + 0.018577... ) = $19,524.78284… Because payments are made at the beginning of the payment period, set the calculator to the BGN mode. N I/Y P/Y C/Y PV PMT FV 32 7.5 4 2 ? ¿ 8 00 0 From the calculator computations shown, we get the PV = 19,524.78284 Step 2: Calculate the present value of this amount at the beginning of the deferred period ( PV def ) Deferral period n = 2 years = 2 × 4 = 8 quarterly periods PV def = PV annuity (1 + i ) n = 19,524.78284…(1 + 0.018577...) -8 = $16,851.31476… = $16,851.31. N I/Y P/Y C/Y PV PMT FV 8 7.5 4 2 ? 0 19,524.78284. .. From the calculator computations shown, we get the PV = ¿ 16,851.31476 Therefore, the purchase price of the deferred annuity is $16,851.31. Review Exercise 11, Solution 5: This is a general deferred annuity due as: Payments are made at the beginning of each payment period (monthly) Compounding period (annually) ≠ payment period (monthly) The deferred period is 2 years.
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