Math! plz help!

posted by .

When Cody's son was born, he put $4,500 in an investment that earns 7% compounded semi-annually. This investment will mature when his son turns 18 and will go straight into an annuity at 4.75% compounded and paying out quarterly at the end of the period. The investment was to help pay for his 4-years of college. Find the size of these quarterly payments received by Cody's son during his college stay.

  • Math! plz help! -

    The first part seems easy enough, but we're not at all sure about the second part. The investment is earning 7% compounded semi-annually until he turns 18, so that means the original $4,500 will have become ((1.07)^36) x $4,500 = $51,407.74 on his 18th birthday. So far, so good.

    Now, we're assuming (and we could easily be wrong about this) that this "4.75% compounded and paying out quarterly" means that the annuity is accumulating interest at this rate annually, BUT paying out 16 equal payments over the four years that he's at college - at the end of which time there will be nothing left. We therefore have to find out what each of those payments will be, bearing in mind that the interest will be accumulating on a different amount every quarter. Tricky....

    Suppose the quarterly payment is Q, that the annuity is purchased for A (which we already know is $51,407.74, but A is easier to write), and P is the quarterly interest rate on the annuity (i.e. whatever rate will give us 4.75% per annum). We're also going to assume that he withdraws his quarterly payment at the END of each quarter, so during the first quarter he's earning interest on the full amount. So the amount left at the end of each quarter should be....

    A(1+P) - Q
    (A(1+P) - Q)(1+P) - Q
    ((A(1+P) - Q)(1+P) - Q)(1+P) - Q
    (((A(1+P) - Q)(1+P) - Q)(1+P) - Q)(1+P) - Q

    P is easy enough to find: it is whatever value will give us (1+P)^4 = 1.0475, i.e. P = 1.167%. With that value, the above series of recursive relationships with any given value of Q can be fed into 16 successive cells in a column of Excel easily enough - and we then need to find Q such that the final amount in the 16th cell is zero. Having done just that, we reckon that the quarterly payment to him should be $3,540.91, which would leave him with just one cent in his account at the end of the fourth year. But arriving at that algebraically is beyond us - and obviously you'll need to show your working to get the marks, so the best we can do is show you how the problem might be tackled, and offer a possible answer to check yours against if you can do it. Sorry!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math!

    When Raisel's son was born, she put $7,500 in an investment that earns 5.25% compounded quarterly. This investment will mature when her son turns 18 and will go straight into an annuity at 7.25% compounded and paying out monthly at …
  2. Annuity!

    When Raisel's son was born, she put $7,500 in an investment that earns 5.25% compounded quarterly. This investment will mature when her son turns 18 and will go straight into an annuity at 7.25% compounded and paying out monthly at …
  3. math help plz!

    When Cody's son was born, he put $4,500 in an investment that earns 7% compounded semi-annually. This investment will mature when his son turns 18 and will go straight into an annuity at 4.75% compounded and paying out quarterly at …
  4. Business Algebra

    I need to know the formula for these questions and just how to do them. If you could help please. As a financial planner a client comes to you for investment advice. After meeting with him and understanding his needs, you offer him …
  5. Math

    How to calculate this? 4 year term investment. The investment offers a rate of 2.25% per annum, compounded semi-annually. Another investment offers a rate of 2.25% annum, per compounded quarterly. Final investment offers a rate of
  6. precalc

    A $5000 investment earns 7.2% annual interest, and an $8000 investment earns 5.4%, both compounded annually. How long will it take for the smaller investment to catch up to the larger one?
  7. pre calculus

    Which is worth more after 5 years, an investment of $1000 at 5% interest compounded semi - annually(twice a year). or an investment of $1000 at 5% interest compounded continuously?
  8. math

    RM65000 will be invested for 6 years 9 months. if the investment will be offered 5% compounded semi annualy for the first 2 years, 6% compounded monthly for the next 18 months and 7% compounded daily for the rest of the period ,find …
  9. math

    RM65000 will be invested for 6 years 9 months. if the investment will be offered 5% compounded semi annualy for the first 2 years, 6% compounded monthly for the next 18 months and 7% compounded daily for the rest of the period ,find …
  10. interest

    Perry has an opportunity to put $12,000 into an investment with an APR of 5.6% compounded annually. How long will it take his investment to double?

More Similar Questions