1215

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) $154,312.20.

B) $95,815.74.

C) $87,105.21.

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

1215

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) $36,577.

B) $41,577.

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.

1215

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) $159,374.

B) $175,312.

C) $110.000.

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

1215

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

A) $1,000.

B) $900.

C) No solution.

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

1215

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) $55,364.

C) $62,285.

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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.

1215

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) $1,080,000.00.

C) $924,423.70.

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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.

1215

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) 27 years.

B) 87 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.

1215

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) $100,135.

B) $901,060.

C) $90,106.

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

1215

An investor wants to receive $1,000 at the beginning of each of the next ten years with the first payment starting today. If the investor can earn 10 percent interest, what must the investor put into the account today in order to receive this $1,000 cash flow stream?

A) $6,759.

B) $6,145.

C) $7,145.

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This is an annuity due problem. There are several ways to solve this problem.

Method 1:

PV of first $1,000 = $1,000
PV of next 9 payments at 10% = 5,759.02
Sum of payments = $6,759.02

Method 2:

Put calculator in BGN mode.
N = 10; I = 10; PMT = -1,000; CPT → PV = 6,759.02
Note: make PMT negative to get a positive PV. Don’t forget to take your calculator out of BGN mode.

Method 3:

You can also find the present value of the ordinary annuity $6,144.57 and multiply by 1 + k to add one year of interest to each cash flow. $6,144.57 × 1.1 = $6,759.02.

1215

An investor purchases a 10-year, $1,000 par value bond that pays annual coupons of $100. If the market rate of interest is 12%, what is the current market value of the bond?

A) $887.

B) $1,124.

C) $950.

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Note that bond problems are just mixed annuity problems. You can solve bond problems directly with your financial calculator using all five of the main TVM keys at once. For bond-types of problems the bond’s price (PV) will be negative, while the coupon payment (PMT) and par value (FV) will be positive. N = 10; I/Y = 12; FV = 1,000; PMT = 100; CPT → PV = –886.99.