Financial Mathematics for Real Estate InvestmentWeek 3

Four Main Topics to CoverMortgage loan fundamentals – Time Value of MoneyFixed interest mortgageAdjustable and floating rate mortgageMortgage: an additional Concept

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

Future Value: General EquationnniPVFV)1(

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

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.

Future ValueOur general equation becomes:where m = number of compounding intervals in a yearmnnmiPVFV1

is also called the period rateFor Example 1:= 100(1.62889)= $162.89mi2552.101100FV

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.

Spreadsheet FunctionFor complex analysis, Excel is much better than the financial calculator. It is far more powerful and capable.

Present ValueDiscounting: Converting Future Cash Flows to the PresentGeneral Equationnni)(11FVPV

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

AnnuityLevel Cash Flow StreamTerminatesOrdinary AnnuityCash flows begin one period from todayAnnuity DueCash flows begin immediately

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

Future Value: Annuity – Monthly= 200(88.5745)= $17,714.9012.15112.151200FV125

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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- Fall '13