Reading 5: The Time Value of Money-LOS e, (Part 2)习题精选 payments, ordinary, interpret, div, class

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Session 2: Quantitative Methods: Basic Concepts
Reading 5: The Time Value of Money

LOS e, (Part 2): Calculate and interpret an ordinary annuity and an annuity due.

 

 

 

An annuity will pay eight annual payments of $100, with the first payment to be received three years from now. If the interest rate is 12% per year, what is the present value of this annuity? The present value of:

A) a lump sum discounted for 3 years, where the lump sum is the present value of an ordinary annuity of 8 periods at 12%.

B) an ordinary annuity of 8 periods at 12%.

C) a lump sum discounted for 2 years, where the lump sum is the present value of an ordinary annuity of 8 periods at 12%.

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The PV of an ordinary annuity (calculation END mode) gives the value of the payments one period before the first payment, which is a time = 2 value here. To get a time = 0 value, this value must be discounted for two periods (years).

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If 10 equal annual deposits of $1,000 are made into an investment account earning 9% starting today, how much will you have in 20 years?

A) $35,967.

B) $42,165.

C) $39,204.

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Switch to BGN mode. PMT = –1,000; N = 10, I/Y = 9, PV = 0; CPT → FV = 16,560.29. Remember the answer will be one year after the last payment in annuity due FV problems. Now PV₁₀ = 16,560.29; N = 10; I/Y = 9; PMT = 0; CPT → FV = 39,204.23. Switch back to END mode.

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Bill Jones is creating a charitable trust to provide six annual payments of $20,000 each, beginning next year. How much must Jones set aside now at 10% interest compounded annually to meet the required disbursements?

A) $87,105.21.

B) $154,312.20.

C) $95,815.74.

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N = 6, PMT = -$20,000, I/Y = 10%, FV = 0, Compute PV → $87,105.21.

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What is the present value of a 12-year annuity due that pays $5,000 per year, given a discount rate of 7.5%?

A) $41,577.

B) $36,577.

C) $38,676.

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Using your calculator: N = 11; I/Y = 7.5; PMT = -5,000; FV = 0; CPT → PV = 36,577 + 5,000 = $41,577. Or set your calculator to BGN mode and N = 12; I/Y = 7.5; PMT = -5,000; FV = 0; CPT → PV = $41,577.

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Consider a 10-year annuity that promises to pay out $10,000 per year; given this is an ordinary annuity and that an investor can earn 10% on her money, the future value of this annuity, at the end of 10 years, would be:

A) $175,312.

B) $110.000.

C) $159,374.

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N = 10; I/Y = 10; PMT = -10,000; PV = 0; CPT → FV = $159,374.

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What is the present value of a 10-year, $100 annual annuity due if interest rates are 0%?

A) $900.

B) $1,000.

C) No solution.

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When I/Y = 0 you just sum up the numbers since there is no interest earned.

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What is the maximum an investor should be willing to pay for an annuity that will pay out $10,000 at the beginning of each of the next 10 years, given the investor wants to earn 12.5%, compounded annually?

A) $52,285.

B) $62,285.

C) $55,364.

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Using END mode, the PV of this annuity due is $10,000 plus the present value of a 9-year ordinary annuity: N=9; I/Y=12.5; PMT=-10,000; FV=0; CPT PV=$52,285; $52,285 + $10,000 = $62,285.

Or set your calculator to BGN mode then N=10; I/Y=12.5; PMT=-10,000; FV=0; CPT PV= $62,285.

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Justin Banks just won the lottery and is trying to decide between the annual cash flow payment option or the lump sum option. He can earn 8% at the bank and the annual cash flow option is $100,000/year, beginning today for 15 years. What is the annual cash flow option worth to Banks today?

A) $855,947.87.

B) $924,423.70.

C) $1,080,000.00.

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First put your calculator in the BGN.

N = 15; I/Y = 8; PMT = 100,000; CPT → PV = 924,423.70.

Alternatively, do not set your calculator to BGN, simply multiply the ordinary annuity (end of the period payments) answer by 1 + I/Y. You get the annuity due answer and you don’t run the risk of forgetting to reset your calculator back to the end of the period setting.

OR N = 14; I/Y = 8; PMT = 100,000; CPT → PV = 824,423.70 + 100,000 = 924,423.70.

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If an investor puts $5,724 per year, starting at the end of the first year, in an account earning 8% and ends up accumulating $500,000, how many years did it take the investor?

A) 87 years.

B) 27 years.

C) 26 years.

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I/Y = 8; PMT = -5,724; FV = 500,000; CPT → N = 27.

Remember, you must put the pmt in as a negative (cash out) and the FV in as a positive (cash in) to compute either N or I/Y.

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If $2,000 a year is invested at the end of each of the next 45 years in a retirement account yielding 8.5%, how much will an investor have at retirement 45 years from today?

A) $901,060.

B) $100,135.

C) $90,106.

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N = 45; PMT = –2,000; PV = 0; I/Y = 8.5%; CPT → FV = $901,060.79.