Presentation on theme: "Chapter ChEn 4253 Terry A. Ring"— Presentation transcript:
1 Chapter 23.5 -23.9 ChEn 4253 Terry A. Ring Time Value of MoneyChapterChEn 4253Terry A. Ring
2 Examples of Time Value of Money Saving AccountInterest increases the amount with timeLoanPayment amountRetirement AnnuityPays out constant amount per monthPays out an amount that increases with inflation per month
3 Interest % interest Time over which it is compounded Day, Week, Month, quarter or yearTwo types of interestSimple Interest – rarely usedCompound InterestBe careful with interestCredit card statement 1.9% per month = 22.8% per year simple interest, IS=niCredit card statement 1.9% per month = 25.34% per year compound interest, IC=[(1+i)n-1]
4 Some Nomenclature F= Future value P=Present value i= interest rate for interest periodr=nominal interest rate (%/yr)ny= no. of yearsn= no. of interest periods
5 Interest Simple interest Compound Interest F=(1+n*i)PCompound InterestF=(1+i)nPAllows present or future value to be determinedCan be inverted to give present value associated with a discount factorNominal Interest (simple interest when period is not 1 yr)r =i*mm= periods per yearEffective Interest Rate (compound interest when period is not 1 yr)ieff= (1+r/m)m-1Continuous Compoundingieff==exp(r) - 1
7 Present Value/Future Value Determine the Present Value of an investment (or payment) in the Future.You are due a $10,000 signing bonus to be paid to you after you have completed 2 yrs of service with your new company. What is the present value of that bonus given 7% interest?Determine the Future Value of an investment made todayWhat is $10,000 worth if kept in a bank for 10 years at 3%/yr (compound) interestPresent value of retirement fund is $300,000. What will it be worth when I am 64 years old.
8 Student LoanGet $10,000 in August Collects interest at 5% until graduation August What amount do you owe upon graduation?F=(1+i)nP =(1+0.05)4 $10,000=$12,160
9 Annuity Series of Single payments, A, made at fixed time periods Examples – Installment LoansStudent Loan RepaymentMortgage LoanCar LoanRetirement – old systemAssumes periodic Compound Interest and payment at end of first perioddiscrete uniform-series compound-amount factorF=A[(1+i)n-1]/iPresent Worth of AnnuityP=F/(1+i)n
10 Annuity Types Mix and match interest and payment schedules Compound InterestDiscrete – monthly, quarterly, semi-annually annuallyContinuousPaymentsDiscrete – monthly, quarterly, semi-annually, annuallyContinuously
11 Annuity Tablei=r/m=periodic interest rate, A = payment per interest period, n=mny number of interest periods, Ā=pÂ=total annual payments per year, p=payments per year, r nominal annual interest rate.
13 Payment for Student Loan Loan amount =$12,160What is payment if annual interest rate is 5% and loan is to be paid off over 10 years using monthly payments?Do this for practice example for practice. Answer is $ (see next slide)Principle is being charged interest each monthEach payment pays interest and lowers principle so interest is lessFix paymentShifts from mostly paying interest toMostly paying principle as time goes on
15 Retirement AnnuityMonthly payments into 401k Account $200/mo at 5%/y interest. After working 25 years, what is value?A= 12*$200N=25i=0.05F=A[(1+i)n-1]/i= $1,145,000Present value of all that investment on your first day of workP=F/(1+i)n=$33,830
16 Compare two alternative pumps Pump A Pump BInstalled Cost $ 20, $ 25,000.00Yearly maintenance $ 4, $ 3,000.00Service Life (yr)Salvage Value $ $ 1,500.00Interest Rate 6.8% 6.8%Life of Plant (yr)
17 Determine Present Value Each PurchasesEach Sale of Salvage EquipmentAll Annual Payments to for MaintenanceAdd them upPurchases are negativeSales are positive