Wk3_-_Financial_Mathematics_for_Real_Estate_Investment.pdf - Financial Mathematics for Real Estate Investment Week 3 Four Main Topics to Cover Mortgage

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Financial Mathematics for Real Estate InvestmentWeek 3
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Four Main Topics to CoverMortgage loan fundamentals – Time Value of MoneyFixed interest mortgageAdjustable and floating rate mortgageMortgage: an additional Concept
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Mortgage loan fundamentals: time value of moneyCompound InterestEarning Interest on InterestBasic ComponentsPV = Initial Depositi= Interest Raten = Number of YearsFVn= Value at a specified future period
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Future Value: General EquationnniPVFV)1(
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Future ValueExample 3.1:What is the value at the end of year 5 of $100 deposited today if the interest rate is 10% compounded annually?FV5= $100(1.10)5= $100(1.61051)= $161.05
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Future Value: Compounding FrequencySemi-Annual CompoundingIn Example 3-1, what if interest were paid semi-annually instead of annually?There would be two compounding periods in each year.There would be a periodic rate to match the multiple compounding periods.The time period would be doubled.Most importantly, the future value would be higher. Additional compounding periods will effect the final result.
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Future ValueOur general equation becomes:where m = number of compounding intervals in a yearmnnmiPVFV1
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is also called the period rateFor Example 1:= 100(1.62889)= $162.89mi2552.101100FV
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Future ValueNotice the difference in Future Value when multiple compounding periods are used:$162.89 vs. $161.05This shows the effect of earning interest on interest. The more compounding periods there are per year, the higher the future value will be.
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Spreadsheet FunctionFor complex analysis, Excel is much better than the financial calculator. It is far more powerful and capable.
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Present ValueDiscounting: Converting Future Cash Flows to the PresentGeneral Equationnni)(11FVPV
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Present ValueExample 3.2:What is the value today of $2,000 you will receive in year 3 if the interest rate is 8% compounded annually?= 2000(.79383)= $1587.663(1.08)12000PV
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AnnuityLevel Cash Flow StreamTerminatesOrdinary AnnuityCash flows begin one period from todayAnnuity DueCash flows begin immediately
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Future Value: AnnuityExample 3.3:What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15% interest rate?= 200(6.74238)= $1348.48.151.15)(1200FVA5
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Future Value: Annuity – Monthly= 200(88.5745)= $17,714.9012.15112.151200FV125
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Present Value: AnnuityExample 3.4:If you had the opportunity to purchase a $500 per year, ten-year annuity, what is the most you would pay for it? The interest rate is 8%.
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