аЯрЁБс;ўџ $ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ§џџџџџџџўџџџўџџџ  !"#ўџџџ%ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџRoot Entryџџџџџџџџџџџџўџџџџџџџџџџџџџџџўџџџџџџџџџџџџџџџўџџџџџџџџџџџџџџџўџџџўџџџўџџџ ўџџџ !"ўџџџ$ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџўџ џџџџ РFMicrosoft Word-Dokument MSWordDocWord.Document.8є9Вq [bёџbDefault$a$A$1$*$/B*CJmH sH aJOJQJPJnHџ^J_HџtHџBA@ђџЁBAbsatz-Standardschriftart<ўђџё<Default Paragraph FontFўFHeading Є№Єx$OJQJCJPJ^JaJ.B. Text body ЄЄx /" List^J@ў2@Caption ЄxЄx $CJ6^JaJ]&ўB&Index $^J‚6џџџџЌ%ф pМ’%%‚‚PGTimes New Roman5Symbol3&Arial9€PalatinoG$ HelveticaArial3Arial5Tahoma5TahomaBаhх 9ƒ9х 99'№0№€ўџр…ŸђљOhЋ‘+'Гй0АHPh t € Œ ˜ Єщ§Present valueSEI0@@@@ўџеЭеœ.“—+,љЎDеЭеœ.“—+,љЎ\щ§щ§ьЅТM П0%Caolan80 $6‚џџџџџџl,4`t4ЩиЈЁXДЈ й Present value The present value is the current value of a single or series of cash payments to be received/paid at future date, discounted at a specified interest rate. Present value= Future Value/(1+rate of interest per period)^No. of periods Example. Mrs Sharon wishes to purchase a car in 3 years from now which will cost her $35,000 in 3 years. If the bank offers her an interest of 4% per annum, what amount he must deposit today so that she can buy car in 3 years time. So amount that Mrs. Sharon must deposit today is the present value of the future sum ($35000) Present value= Future Value/(1+rate of interest)^3 Present value= 35000/(1+0.04)^3 Present value = 35000/1.1249 Present Value = 31,114.87 Present value of annuity The present value of annuity is a single equivalent value of series of equal cash payments to be received / paid at a regular interval on future dates, discounted at a specified interest rate. PV of Ordinary annuity = Annuity * PV of Ordinary Annuity factor Annuity is series of equal sum of money that is received / paid at constant intervals in the future. The annuity factor is calculated as PV of Ordinary Annuity factor = [1-(Discount factor of last year)/ Discount rate] = [1- 1/(1+r)^n]/r (Note: Present value of annuity can be calculated by adding the sum of the present value of each cash flow to be received/paid. PV of Annuity = PV of cash flow1 + PV of cash flow 2 & & & & & & & & .+PV of cash flow n The is the lengthy generally not followed for annuity) Example Mr. Bruce is planning to purchase a pension plan under which he would receive $5000 at the end of every year for next 15 years. What amount should Mr. Bruce pay today (fair value) if the he can earn a 5% per annum? Now the Amount he should pay is the PV of annuity for amount of 5000 and discount rate of 5% PV Annuity Factor= [1- 1/(1+.05)^15]/.05 = 10.3797 The present value of annuity is = 10.3797 * 5000=$51898.29 (Note: When annuity is paid/received at the end of every year its called ordinary annuity. The above formula for PV annuity factor is for PV of ordinary annuity. When annuity is paid/received at the beginning of every year it called annuity due. The formula is for PV annuity due factor = PV of Ordinary Annuity Factor*(1+r) ) Future Value Future value is given sum of money's "worth" at a specified time in the future assuming a certain interest rate. Future value = Original Sum of Money * (1+ interest rate per period)^ No. of periods Example Suppose Mr. Bond have deposited $5,000 in bank account. If my bank offers 8% interest rate annually , how much would Mr. Bond receive after 5 years? The amount Mr. bond would have after 5 years is the future value. Future value = present value * (1+rate of interest)^5 Future value = 5000* (1+0.08)^5 Future value = $7346.64 Future value of annuity Future value of annuity is the future value of a series of payments (annuity) to be received / paid at a regular interval on future dates, compounded at a specified interest rate. FV of ordinary annuity = Annuity * FV Ordinary Annuity factor Annuity is series of equal sum of money that is received / paid at constant intervals in the future. The annuity factor is calculated as FV ordinary Annuity factor = [(1+r)^n-1]/r (Note: FV value of annuity can be calculated by adding the sum of the FV value of each cash flow to be received/paid. FV of Annuity = FV of cash flow1 + FV of cash flow 2 & & & & & & & & .+FV of cash flow n The is the lengthy generally not followed for annuity) Example Mrs. Susan deposit $1000 every year in her bank deposit for next 5 years. What is the amount she will accumulate at the end of five year. Rate of interest is 7%. The amount Mrs. Susan would have after 5 years is the future value of annuity FV annuity factor = {(1+.07)^5-1}/.07 = 5.7507 FV = 1000*5.7507= $5750.70 (Note: When annuity is paid/received at the end of every year it called ordinary annuity. The above formula for annuity factor is for ordinary annuity. When annuity is paid/received at the beginning of every year it called annuity due. 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