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Math Help - Annuities/Compound Interest 10 questions

  1. #1
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    Annuities/Compound Interest 10 questions

    Can anyone help me out w/these?

    1. A 1 year $100,000 T-bill sells at a discount rate of 3.25%. What simple annual interest rate does it pay. (Round to the nearest 100th of a percent.)

    a. 3.36%

    b. 3.14%

    c. 3.25%

    d. None of these


    2. If $10,000 is deposited in a money market account when interest is compounded every month at an annual rate of 5%, the total amount accumulated at the end of 5 years will be: (Round to the nearest cent.)

    a. $12,762.82

    b. $10,210.08

    c. $12,833.59

    d. None of these



    3.. If you invest $5,000 at 4% compounded semiannually, how long will it take for your investment to grow to $8,000? (Round to the nearest year.)

    a. 10 years

    b. 24 years

    c. 6 years

    d. None of these



    4.. How much would you have to invest when you are 20 years old at 6% compounded monthly to end up with a million dollars by age 50? (Round up to the nearest thousand.)

    a. $862,000

    b. $167,000

    c. $175,000

    d. None of these


    5. If you deposit $4,000 in a money market account when interest is compounded quarterly, what annual rate of interest would be required to end up with $8,000 in 5 years? (Round to the nearest 10th of a percent.)

    a. 13.9%

    b. 14.1%

    c. 14.7%

    d. None of these


    6. How much should we deposit now into an account earning 6% interest per year, compounded monthly so that starting one month from now the bank will send us monthly payments of $200 for 5 years? At the end of the five years, the account balance should be depleted to zero. (Round to the nearest cent.)

    a. $11,280.00

    b. $10,396.84

    c. $10,345.11

    d. None of these


    7. How much should be deposited now in an account earning 4.2% interest per year, compounded quarterly so that starting 3 months from now the bank will send us quarterly payments of $150 for 10 years? At the end of that time we would like to have $2,000 left in the account. (Round to the nearest cent.)

    a. $6,246.96

    b. $6,195.73

    c. $4,878.76

    d. None of these




    8.. A newspaper carries advertisements for CD rates / terms for four local banks. Which would be the best deal?

    a. Scrooge Investments -- 4.00% compounded daily

    b. Cloverdale Bank & Trust -- 4.10% compounded quarterly

    c. Omega Savings & Loan -- 4.00% compounded quarterly

    d. Worker’s Credit Union -- 4.10% compounded annually



    9. Midwest Bank & Trust advertises a CD that pays 4.9% APY compounded monthly. What is the effective interest rate? (Round to the nearest 10th of a percent.)

    a. 4.8%

    b. 4.9%

    c. 5.0%

    d. None of these



    10. What would it cost to buy a U.S. Treasury bill that pays $10,000 after 6 months where the simple annual interest rate is 3.75%? (Round to the nearest cent.)

    a. $9,625.45

    b. $9,812.50

    c. $9,815.95

    d. None of these
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  2. #2
    GAMMA Mathematics
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    Let's try these one at a time..

    1. A 1 year $100,000 T-bill sells at a discount rate of 3.25%. What simple annual interest rate does it pay. (Round to the nearest 100th of a percent.)

    a. 3.36%

    b. 3.14%

    c. 3.25%

    d. None of these
    The amount of the the T-bill is irrelevant. I assume the discount rate is simple as well.

    1 - d = \frac{1}{i+1}
    1 + i = \frac{1}{1-d}
    i = \frac{d}{1-d} = \frac{.0325}{1-.0325} = .0336

    ANSWER = A
    Last edited by colby2152; November 29th 2007 at 12:56 PM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by colby2152 View Post
    Let's try these one at a time..



    The amount of the the T-bill is irrelevant. I assume the discount rate is simple as well.

    1 - d = \frac{1}{i+1}
    1 + i = \frac{1}{1-d}
    i = \frac{d}{1-d} = \frac{.0325}{1-.0325} = .0336

    ANSWER = D
    0.0336 is 3.36%

    RonL
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  4. #4
    GAMMA Mathematics
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    2. If $10,000 is deposited in a money market account when interest is compounded every month at an annual rate of 5%, the total amount accumulated at the end of 5 years will be: (Round to the nearest cent.)

    a. $12,762.82

    b. $10,210.08

    c. $12,833.59

    d. None of these
    Follow this formula:

    1 + I = (1 + \frac{i}{m})^{mt}

    Therefore, the accumulation is:

    A = 10,000(1 + \frac{.05}{12})^{12*5} = 12,833.59

    ANSWER = C
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  5. #5
    GAMMA Mathematics
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    Quote Originally Posted by JP101 View Post
    3.. If you invest $5,000 at 4% compounded semiannually, how long will it take for your investment to grow to $8,000? (Round to the nearest year.)

    a. 10 years

    b. 24 years

    c. 6 years

    d. None of these
    Similar to the last problem, but we are solving for time. Also note that this is 4% semiannual interest rate. No where in the problem do you see the word annual.

    8,000 = 5,000(1.04)^{t/2}
    ln(1.6) = \frac{tln(1.04)}{2}
    .47 = .0196t
    t = 23.97 years

    ANSWER = D
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  6. #6
    GAMMA Mathematics
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    Quote Originally Posted by CaptainBlack View Post
    0.0336 is 3.36%

    RonL
    Thanks RonL, I fixed the typo. BTW, I am doing these problems one at a time due to time restrictions.
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