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Herbert J. Bernstein Professor of Mathematics and Computer Science
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90092 MTH 1002 A -- Fundamentals of Mathematics -- Fall 2012
Online Course
Quiz 8

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This is the one of two weekly quizzes for 27 November 2012 for the MTH 1002 course. Please do this quiz after you have completed the rest of assignment 8. If you do not want delayed grading past the end of the semester, you will also have to do the next quiz as well. It should take between one half hour and 2 1/2 hours to complete if you are well prepared, longer if not.

In answer to questions on this page, when you need to show an exponent as in xa show the raised part using ^ and (), as in x^(a). For division, use / and (), as in (x^3-1)/(x-1).

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  1. What is the formula for the future value of an ordinary annuity? Be sure to explain the meaning of each symbol you use in the formula.

  2. What is the formula for the present value of an ordinary annuity? Be sure to explain the meaning of each symbol you use in the formula.

  3. What is the formula for the payment to make to amortize a debt with equal periodic payments. Be sure to explain the meaning of each symbol you use in the formula.

  4. You wish to buy a house for $450,000. You are offered a mortgage for that amount to be paid back over 30 years using even monthly payments monthly based on an annual interest rate of 6%. Compute the monthly payment. Compute the total sum of all payments. Compute the difference between the total sum of all payments and the amount you borrowed (the total Interest). Note that the natural log of 1.005 is .004987541511, that there are 360 months in 30 years, and that e to the power 1.795514944 is 6.022575212. Show your work.

  5. You wish to buy a house for $450,000. You are offered a mortgage for that amount to be paid back over 15 years using even monthly payments monthly based on an annual interest rate of 6%. Compute the monthly payment. Compute the total sum of all payments. Compute the difference between the total sum of all payments and the amount you borrowed (the total Interest). Note that the natural log of 1.005 is .004987541511, that there are 180 months in 30 years, and that e to the power 0.897757472 is 2.454093562 Show your work.

  6. You wish to buy a house for $450,000. You are offered a mortgage for that amount to be paid back over 30 years using even monthly payments monthly based on an annual interest rate of 4.5%. Compute the monthly payment. Compute the total sum of all payments. Compute the difference between the total sum of all payments and the amount you borrowed (the total Interest). Note that the natural log of 1.00375 is .003742986279, that there are 360 months in 30 years, and that e to the power 1.34747506 is 3.84769805 Show your work.

  7. Suppose you are about to retire, and interest rates are a steady, reliable 3%. If you have saved $92606 and expect to live another 20 years. How much can you draw each month from this investment. Give the answer first as a formula with values in place of variables, and then do the actual calculation. In doing the calculation, it helps to note that the log of a power, n, of a, is n time the log of a, that the natural log of 1.0025 is 0.0024968802, that there are 240 months in 40 years, and that e to the power 0.599251247 is 1.820754995 Show your work.

  8. Suppose your employer offers you the chance to put $100 per month of your salary into an 401K that earns a solid, reliable 3% per annum compounded and credited monthly. How much would you have saved in this investment after 40 years. Give the answer first as a formula with values in place of variables, and then do the actual calculation. In doing the calculation, it helps to note that the log of a power, n, of a, is n time the log of a, that the natural log of 1.0025 is 0.0024968802, that there are 480 months in 40 years, and that e to the power 1.198502495 is 3.315148753 Show your work.

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Updated 24 November 2012.