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Math Help - business math

  1. #1
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    business math

    You have just had your 30th birthday. You have two children. One will go to college 10 years from now and require four yearly payments for college expenses of $10000, $11000, $12000 and $13000. The second child will go to college 15 years from now and require four yearly payments for college expenses of $15000, $16000, $17000, and $18000. In addition, you plan to retire in 30 years. You want to be able to withdraw $50000 per year from an account throughout your retirement. You expect to live 20 years beyond retirement. The first withdrawal will occur on your 61st birthday. All savings earn a 13% annual rate of return.

    What equal, annual amount must you save for each of the next 30 years in order to meet these goals?

    I am really lost. I dont know how to solve this question. I only know that i have to calculate the present value of the first and second child and for the retirement annuity. Anyone can guide me with this question pls............

    thanks in advance
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  2. #2
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    Quote Originally Posted by kogi_17 View Post
    You have just had your 30th birthday. You have two children. One will go to college 10 years from now and require four yearly payments for college expenses of $10000, $11000, $12000 and $13000. The second child will go to college 15 years from now and require four yearly payments for college expenses of $15000, $16000, $17000, and $18000. In addition, you plan to retire in 30 years. You want to be able to withdraw $50000 per year from an account throughout your retirement. You expect to live 20 years beyond retirement. The first withdrawal will occur on your 61st birthday. All savings earn a 13% annual rate of return.

    What equal, annual amount must you save for each of the next 30 years in order to meet these goals?
    Ok, I checked my lessons. Here is how I did this:

    Let's get the present value of everything at 30th birthday.

    First, Take the present value of the first child's college expense annuity. A 4 year annuity with first payment of 10000 increasing by 1000 for a term of 4 years.

    Arithmetic Annuity Immediate Present Value

    Use the Present Value button. 13 for interest rate, 10000 for first payment, 4for number of periods, and 1000 for arithmetic payment. We get 33753.92 Present Value at age 40. Now, we need to discount that back to age 30. At 13% universal savings account rate that you give, we get 1/(1.13^10) = 0.294588348 Multiply this by our Present Value at age 40 and we get 9,943.51.

    Now, our 2nd child's annuity is the same parameters as above, but 15000 is the first payment. Simply change your 10000 to 15000 and press Calculate. We get a Present Value at age 45 of 48626.27. Doing our discount factor 15 years back to age 30 gives us 1/(1.13^15) = 0.159890753. Multiply this by our Present Value at age 45 and we get 7774.89.

    Now, our last Present Value to bring back to age 30 is our dad's retirement account. Go here:
    Annuity Immediate Present Value

    Calculate Present Value, 13 for interest rate, 50000 for payment, and 20 for n and press Calculate. Our Present Value is 351237.58 at age 60. We need to bring this back 30 years to our dad's 30th b-day. Discount factor is just like above, 1/(1.13^30) = 0.025565053. Multiply this by our Present Value of retirment payments at age 60, and we get 8979.41.

    Now, we add up our 3 present value of payment streams at age 30 to get:
    9,943.51 + 7774.89 + 8979.41 = 26697.81. Now we forward march and cross the finish line. Your problem asks what EQUAL annual amount does he need to invest to meet this obligation?

    He's age 30 now, and the entire payout ends at age 80. That's a 50 year term.

    Return to this lesson:
    Annuity Immediate Present Value

    This time, calculate payment. Present value is 26697.81, interest rate is 13, and our term is 30. Our term is 30, because your problem stated he wants this money ready at age 60 for his retirement. Press Calculate and our answer is 3561.77.

    Therefore, he would need to deposit 3561.77 on every birthday starting 1 year from now to meet the 2 kids obligations and his retirement obligation.

    Let me know if this doesn't match your answer key, or doesn't sound right.
    Last edited by mathceleb; August 12th 2009 at 11:51 PM.
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  3. #3
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    Thanks for the help.

    I tried doing this question and my answer is different. I get a total around$8561. I like to find out when finding the present value for the childrens college payments, dont I need to find the present value for all the four yearly payment separately as it is uneven cash flow? As from what I understand that it is not even cash flow as we do not look at the amount that it is incresing but the amount itself.

    Based on my notes, if to use the even flow of cash formula to calculate means that all the four periods must have same amount of money. For example $1000 for all four periods (same amount of money). That means we do not use the even flow of cash flow formula in this situation as all the values are different ($10000, $11000, $12000 and $13000). Could you please explain.

    Thanks in advance
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  4. #4
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    Quote Originally Posted by kogi_17 View Post
    Thanks for the help.

    I tried doing this question and my answer is different. I get a total around$8561. I like to find out when finding the present value for the childrens college payments, dont I need to find the present value for all the four yearly payment separately as it is uneven cash flow? As from what I understand that it is not even cash flow as we do not look at the amount that it is incresing but the amount itself.

    Based on my notes, if to use the even flow of cash formula to calculate means that all the four periods must have same amount of money. For example $1000 for all four periods (same amount of money). That means we do not use the even flow of cash flow formula in this situation as all the values are different ($10000, $11000, $12000 and $13000). Could you please explain.

    Thanks in advance
    2 things:

    1) Did you see the link I provided - Arithmetic Annuity Immediate Present Value

    That is for an arithmetic annuity, and it shows you the math work involved to calculate it. i.e., one that starts off at one amount, and each annuity payment after that is an arithmetic factor of the first. It can go up or down, in this case, it goes up by 1000.

    Ignoring that formula, think of it this way:

    10000/1.13 + 11000/(1.13^2) + 12000/(1.13^3) + 13000/(1.13^4) = 33753.92

    You may want to google arithmetic annuities to confirm what I'm showing you.

    2) Is there an answer in the back of the book that tells if one of us is right, or none of us is right?
    Last edited by mathceleb; August 12th 2009 at 11:50 PM.
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  5. #5
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    Thanks for explaining. I understand the method you used. There are no answers provided in the book. When I compared my answers with my friends, all of us have different answers.
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  6. #6
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    Quote Originally Posted by kogi_17 View Post
    Thanks for explaining. I understand the method you used. There are no answers provided in the book. When I compared my answers with my friends, all of us have different answers.
    Looking over the problem again, the only thing that could be different in my math is performing an annuity due on the 2 student loan annuities. Which would just involve multiplying each of their present values before discounting back to 0 by 1.13.
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