cJean Marie Linhart 2008Math 166 Finance IIReview question:(From Barron’s GRE 2009 Test Prep Guide – most GRE practice tests have a questionlike this on them, which is a pretty good indication that this is also a common GREquestion.)Of the 200 seniors at Monroe High School, exactly 40 are in the band,60 a re in the orchestra and 1 0 are in both. How many students arein neither the band nor the orchestra?a) 80 b) 90 c) 10 0 d) 110 e) 120(Also from the Barron’s GRE 2009, and, again, a common theme for a problem.)Jordan has taken 5 math tests so far this semester If he gets a 70 onhis next test, it will lower the average (arithmetic mean) of his testscores by 4 points. What is his average now?a) 74 b) 85 c) 86 d) 90 e) 941. If you need to have $150,000 for when your newborn goes to collegein 18 years, how much do you need to save every month if you canget a 6 % annual return compounded monthly?How much interest do you earn over the entire 18 years?1How much interest do you earn during the 10th year?2. If you purchase an ordinary annuity for $100,000 at 7% per yearcompounded quarterly for 20 years, what is the quarterly paymentyou will receive over the 20 year period?What is the interest earned during the first quarter of the fifth year?3. You have a choice between taking a lump-sum payment of $500,000or being paid $50,00 0 per year for 15 years. Assuming you canmake 8.3% annual interest compounded annually, which of these isthe better deal?24. Jim has racked up $ 10,000 in credit card debt which he will pay offin 5 months by living with his parents and working two jobs whichwill also have the salutary effect of preventing him from charginganything new – incurring new debt – on his credit card). His inter-est rate is 18.2% annually, and is comp ounded monthly. Make anamortization table for his repayment of this debt.Note: You take care of roundoff errors in the last line of the amor-tization table.PaymentEnd of Repayment Interest toward OutstandingPeriod made charged principal principal0 — — — $10,000.0012345 $0,000.0035. (True story) Jean Marie bo ught a house, making her first monthlymortgage payment at the end of January 2004. The purchase pricewas $12 8,000. She made a 5% downpayment, financed 80% of the128,000 with a 5.75% annual percentage rate loan for 30 years (com-pounded monthly) and the remaining 15% at 6.875% annual per-cent age rate loan for 15 years (compounded monthly). Splitting theloans like this allowed her to put less tha n 20% down and to alsoavoid private mortgage insurance which is required if a loan is madefor more than 80% of a home’s value. (PMI insurance is annoying,expensive and hard to get rid of once you have reached 20% equityin the house...) What are her two payments?How much equity does she have in the house now ( November, 2008)if we assume the house’s value has not changed since purchase andthat Jean Marie has made the minimum payments?Equity is the amount of the house that one owns. Since we areassuming the house has not appreciated (increased in value) or de-preciated (decreased in va lue) this would be the amount of principalshe has paid off plus the amount o f the downpayment. If the ho usehas appreciated, we have to add in the amount of appreciation. Ifthe house has depreciated, we have to subtract off the amount ofthe depreciation.If the ho use has appreciated to $150,0 00, how much equity does shehave assuming she made the minimum payments?4Being a frugal mathematician, Jean Marie has been attemptingto pay the higher interest rate loan off early by making an extra$150/month payment toward principal since the loan’s inception.How much does she currently owe on this loan?Given the higher payments Jean Marie has been making on thehigher interest rate loan, a nd given that the house is currently worthabout $150,000, what is her equity in the house?How much interest has Jean Marie paid on each of the two loans(and in total) on the house so far?55. Jane has racked up $13,000 in credit card debt which she will pay offin 6 months by living with her parents and working two jobs, whichwill also have the salutary effect of preventing her from charginganything new – incurring new debt – on her credit card. Her inter-est rate is 16.4% annually, and is comp ounded monthly. Make anamortization table for her repayment of this debt.Note: You take care of roundoff errors in the last line of the amor-tization table.PaymentEnd of Repayment Interest toward OutstandingPeriod made charged principal principal0 — — — $13,000.00123456 $0,000.006The TVM SolverTVM stands fo r the Time Value of Money.N – number of compoundings (payments)I% – percent, not decimal, interest rate (per compounding period aswe are using it). You enter 10 for 10% not 0.1 here.PV – previous va lue or original principalPMT – payment (on an annuity, mortgage payment, amount savedevery month)FV – Future valueP/Y – Payments per year (we are not using this)C/Y – Compoundings (also called conversions) per year (we are notusing this)PMT:END BEGIN tells whether the payment is at the end of thecompounding period or at the beginning – we consistently have hadit at the END of the period.The calculator uses a cash flow convention, and consequently so mustwe. Money is negative when it leaves your hands for the bank, andit is positive when it comes back to you. The PV on a mortgageloan is money that the bank gives me, so that is positive, but mymonthly payment is made to the bank, so that is negative. Likewise,if I am saving for college, the monthly payment I make is negative,but the a mount I have accumulated at the end is positive.One of my favorite personal finance websites is http://www.fool.com.You may want to read their investing basics and personal