mouse123

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) $6,145.

B) $6,759.

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.

mouse123

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) $1,124.

B) $887.

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.

mouse123

Given investors require an annual return of 12.5%, a perpetual bond (i.e., a bond with no maturity/due date) that pays $87.50 a year in interest should be valued at:

A) $70.

B) $700.

C) $1,093.

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87.50 ÷ 0.125 = $700.

mouse123

What is the total present value of $200 to be received one year from now, $300 to be received 3 years from now, and $600 to be received 5 years from now assuming an interest rate of 5%?

A) $980.89.

B) $905.87.

C) $919.74.

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200 / (1.05) + 300 / (1.05)3 + 600 / (1.05)5 = 919.74.

mouse123

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) $62,285.

B) $52,285.

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.

mouse123

Find the future value of the following uneven cash flow stream. Assume end of the year payments. The discount rate is 12%.

Year 1	-2,000
Year 2	-3,000
Year 3	6,000
Year 4	25,000
Year 5	30,000

A) $58,164.58.

B) $65,144.33.

C) $33,004.15.

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N = 4; I/Y = 12; PMT = 0; PV = -2,000; CPT → FV = -3,147.04
N = 3; I/Y = 12; PMT = 0; PV = -3,000; CPT → FV = -4,214.78
N = 2; I/Y = 12; PMT = 0; PV = 6,000; CPT → FV = 7,526.40
N = 1; I/Y = 12; PMT = 0; PV = 25,000; CPT → FV = 28,000.00
N = 0; I/Y = 12; PMT = 0; PV = 30,000; CPT → FV = 30,000.00
Sum the cash flows: $58,164.58.
Alternative calculation solution: -2,000 × 1.124 − 3,000 × 1.123 + 6,000 × 1.122 + 25,000 × 1.12 + 30,000 = $58,164.58.

mouse123

An investor deposits $10,000 in a bank account paying 5% interest compounded annually. Rounded to the nearest dollar, in 5 years the investor will have:

A) $12,763.

B) $12,500.

C) $10,210.

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PV = 10,000; I/Y = 5; N = 5; CPT → FV = 12,763.
or: 10,000(1.05)5 = 12,763.

mouse123

If a person needs $20,000 in 5 years from now and interest rates are currently 6% how much do they need to invest today if interest is compounded annually?

A) $14,945.

B) $14,683.

C) $15,301.

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PV = FV / (1 + r)n = 20,000 / (1.06)5 = 20,000 / 1.33823 = $14,945
N = 5; I/Y = 6%; PMT = 0; FV = $20,000; CPT → PV = -$14,945.16

mouse123

What will $10,000 become in 5 years if the annual interest rate is 8%, compounded monthly?

A) $14,693.28.

B) $14,802.44.

C) $14,898.46.

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FV(t=5) = $10,000 × (1 + 0.08 / 12)60 = $14,898.46
N = 60 (12 × 5); PV = -$10,000; I/Y = 0.66667 (8% / 12months); CPT → FV = $14,898.46

mouse123

If $10,000 is invested in a mutual fund that returns 12% per year, after 30 years the investment will be worth:

A) $10,120.

B) $299,599.

C) $300,000.

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FV = 10,000(1.12)30 = 299,599
Using TI BAII Plus: N = 30; I/Y = 12; PV = -10,000; CPT → FV = 299,599.