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# Class Note for MATH 2303 at UH

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This 11 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 17 views.

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Date Created: 02/06/15

Math 2303 Math of Finance Using your calculator with more complex formulas First you must have a scienti c calculator A fourfunction calculator will not be suf cient for some of the problems we will work Also no graphing calculators will be allowed on the test There are two basic formulas of calculators With one of them you put in the function rst and then the number With the other you put in the number and then the function You need to know which type of calculator you have Try both ofthese 25 25f If this one gave you 5 you have a function rst calculator If this one gave you 5 you have a number rst calculator Now for some practice 1 Example 1 Evaluate 54 33 BTW 7 is this rational or irrational 1 312 57 2 Example 2 Evaluate 210 63 3 5 Now for the formulas Simple interest this formula gives the amount of interest ea1ned on a principal amount P that is invested at interest rate r for t years Example 3 Find the simple interest earned on 2500 invested at 35 interest for 2 years Example 4 Same situation but suppose the money is only invested for siX months The accumulated amount formula gives you the total amount in the account after interest has been added The total will include the amount you put in AND the amount the bank put in as interest Example 5 Suppose you invest 5000 at 25 interest for 4 years How much money is in the account at the end of the 4 years If a bank pays compound interest you do not have to wait until the end of a year to earn money on your investment They will pay interest periodically throughout the year Then you will be earning interest on the money you put in the bank AND on the money they give you as interest Interest can be given semiannually twice a year quarterly four times a year monthly 12 times a year or daily 360 times a year The future value compound interest formula will give you the amount of money both original investment and interest under the interest conditions given for the speci ed number of years Example 6 A bank pays its investors compound interest How much money will be in an account at the end of 5 years if 12000 was invested at 3 interest compounded quarterly Example 7 Suppose in example 6 that the money was invested for only 18 months What would be the amount in the account at the end of that time The present value formula answers this question How much money needs to be invested in an account TODAY as in now 7 at the present moment at these compound interest conditions in order to have a certain amount of money available at a designated time in the future Example 8 How much money should be invested today at 6 interest compounded monthly if you wish to have 10000 in an account in 4 years The effective rate formula gives the answer to this question What simple interest rate would I need to earn in order to earn as much interest as I can earn at a given compound interest rate Example 9 Find the effective rate if money is invested at 64 interest compounded quarterly Most people don t have large sums of money to invest all at once More typically people put away smaller amounts of money periodically These are called annuities An annuity is simply a stream of periodic payments The future value of an annuity formula will give the amount in an account if you invest the same amount of money at the end of each period for the speci ed period of time The periods for making payments and paying interest must be the same Example 10 Find the future value of an annuity if you invest 275 per quarter in an account that pays 5 interest compounded quarterly for 6 years Example 11 Find the future value of an annuity if you invest 50 per month in an account that pays 4 interest compounded monthly for 20 years The present value of an annuity gives the cash price for an item Suppose you know your friend s car payment and interest condition Using this formula you can gure out how much she paid for her car Example 12 Find the cash price of a car if the monthly payment is 550 and the interest rate on the car loan was 875 compounded monthly for 6 12 years Example 13 Suppose you made a 30000 down payment on your house and the monthly payments are 158475 Your interest rate is 72 and you nanced the house for 30 years What was the purchase price cash price of the house The monthly payment formula can tell you how much you should expect to pay per month when you borrow a certain amount of money under given interest conditions This is often referred to as an amortization formula Example 14 Suppose you bought a car for 36000 You had a tradein allowance of 4000 and you financed the rest Your interest rate was 875 compounded monthly and you chose to make payments for 6 years What is your monthly payment on your new car Example 15 Suppose you buy a house for 600000 You make a 10 down payment and nance the rest Your interest rate is 575 compounded monthly for 30 years What is your monthly payment Finally we ll look at the taxfree yield formula Some investments give regular income that you have to pay taxes on Some investments give taxfree income On these investments you don t have to pay income taxes on the interest you earn This formula tells you what taxfree rate is equivalent to a given taxable interest rate In this formula Tf is the taxfree rate Ta is the taxable rate and F is the federal income tax bracket of the person making the investment Example 16 Suppose you are in a 35 tax bracket and you are considering both taxable and a taxfree investments for your 50000 The taxable investment yields 65 How much will a taxfree investment need to yield to be equivalent

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