002. TIME VALU OF MONEY

TIME VALUE OF MONEY : 

TIME VALUE OF MONEY

1. SIMPLE INTEREST : 

1. SIMPLE INTEREST Always interest is calculated on basic/principal amount. FORMULA : I = Pit A = P+I [or] A = P+Pit = P[1+it] Were: P = Principal Amount I = Interest Amount T = No of years A = Accumulated/ Total amount

Example:- Mr. X deposited Rs 1000 @ 10% pa [SI] what will be the total amount received after 2 years ? : 

Example:- Mr. X deposited Rs 1000 @ 10% pa [SI] what will be the total amount received after 2 years ? P = 1000 I = Pit 1000 10% 2 = 200 A = P+I = 1000 + 200 = 1200 A = P[1+it] = 1000{1+0.1 2} = 1000{1.2}=1200 Note : 1. Simple interest is always on basic principal amount. 2. Interest amount per annum is constant. 0 1 2

2. COMPOUNDING INTEREST : 

2. COMPOUNDING INTEREST It is the process of investing principal amount as well as reinvesting interest earned there on for a particular year.

EFFECTIVE RATE OF INTEREST PER ANNUM : 

EFFECTIVE RATE OF INTEREST PER ANNUM Interest: If interest is payable { M } times in a year then effective rate of interest per annum is mn 1+ r 1 m Principal Amount: Effective interest rate P.A ERI P.A = INTEREST AMT PER ANNUM PRINCIPAL AMOUNT 100

FUTURE VALUE OF SINGLE CASH FLOW ;IF INTEREST IS COMPOUNDING ON ANNUALLY BASIS. : 

FUTURE VALUE OF SINGLE CASH FLOW ;IF INTEREST IS COMPOUNDING ON ANNUALLY BASIS. Formula: n Fvf = Pv [ 1+r ] Fvn = Pv . Fvf n Fvf = [ 1 + r ] Were: Fvn = Future value after n year Pv = Present value r = Rate of interest P.A n = No of years Fvf = Future Value Factor Note : Fvf table explains what will be future value of today’s Re.1

FUTURE VALUE OF A SINGLE CASH FLOW ; IF INTEREST IS PAYABLE “ m times” IN A YEAR. : 

FUTURE VALUE OF A SINGLE CASH FLOW ; IF INTEREST IS PAYABLE “ m times” IN A YEAR. FORMULA: mn Fvf = Pv { 1 + r / m }

PRESENT VALUE OF SINGLE FUTURE CASH FLOW ; IF INTEREST IS PAYABLE COMPOUNDING ON ANUALLY BASIS. : 

PRESENT VALUE OF SINGLE FUTURE CASH FLOW ; IF INTEREST IS PAYABLE COMPOUNDING ON ANUALLY BASIS. FORMULA: n Fv = Pv { 1 + r } Pv = Fv n { 1 + r } Fv . 1 n { 1+ r } Pvf tables explains what will be the today’s Value of future Re.1

PRESENT VALUE OF FUTURE SINGLE CASH FLOW IF INTEREST IS COMPOUNDING “m times” IN A YEAR. : 

PRESENT VALUE OF FUTURE SINGLE CASH FLOW IF INTEREST IS COMPOUNDING “m times” IN A YEAR. FORMULA: mn Fv { 1+ r / m } Pv = Fv mn { 1+ r / m }

ANNUITY: Means an even cash flow occurs with fixed intervals for a particular period. : 

ANNUITY: Means an even cash flow occurs with fixed intervals for a particular period. ORDINARY ANNUITY: An even cash flow occurs at the end of each year for a particular period. ANNUITY DUE: An even cash flow occurs at the begging of each year for “n” periods.

FUTURE VALUE OF AN ORDINARY ANNUITY IN CASE OF EVEN CASH FLOW : 

FUTURE VALUE OF AN ORDINARY ANNUITY IN CASE OF EVEN CASH FLOW FORMULA n-1 n-2 n-n Tfcf = Cf1 { 1+ r } + { 1+ r } + - - - - - - - - - - - - + Cfn { 1 + r } 1. n Tfv of Cf = CFPA {1 + r } – 1 r 2. Note: In case of future value of uneven cash flow ordinary annuity formula – 2 is not applicable.

FUTURE VALUE OF ANNUITY DUE IN CASE OF EVEN CASH FLOW : 

FUTURE VALUE OF ANNUITY DUE IN CASE OF EVEN CASH FLOW FORMULA n-0 n-1 n-[ n-1 ] Tfv of CF = CF0 { 1 + r } + Cf1 { 1 + r } + - - - - - - + Cfn { 1 + r } 1. n 1 Tfv of CF = CFPA { 1 + r } – 1 { 1 + r } r 2. Note: In case of future value of annuity due uneven cash flow formula – 2 is not applicable.

PRESENT VALUE OF ORDINARY ANNIUITY ; IN CASE CASH FLOW ARE EVEN CASH FLOWS AT END OF YEAR. : 

PRESENT VALUE OF ORDINARY ANNIUITY ; IN CASE CASH FLOW ARE EVEN CASH FLOWS AT END OF YEAR. FORMULA 1. Tpv of CF = CFPA AF [ r, n ] 2. Tpv of CF = CF1 + CF2 + - - - - - - - - + CFn 1 2 n { 1 + r } { 1 + r } { 1 + r } 3.

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n Tpv of CF = ∑ Cash Flow { cft } t=1 t { 1 + r } 4. n Tpv of Cf = CFPA { 1 + r } – 1 n r { 1 + r } 5. Note: In case of present value of uneven cash flow; Formula 2 & 5 will not applicable.

PRESENT VALUE OF ANNUITY DUE; IN CASE CASH FLOW ARE EVEN CASH FLOW OCCURS AT THE BEGNING OF EACH YEAR. : 

PRESENT VALUE OF ANNUITY DUE; IN CASE CASH FLOW ARE EVEN CASH FLOW OCCURS AT THE BEGNING OF EACH YEAR. 1. Tpv of CF = CFPA 1 + AF { r, n -1 } 2. Note: In case of present value of uneven cash flow for annuity due, formula 2 is not applicable.

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We are to take care of ourselves – that much we can do – and give up attending to others for a time. Let us perfect the means; the end will take care of itself. For the world can be good and pure, only if our lives are good & pure. It is an effect , and we the means. Therefore, let us purify ourselves. Let us make our – Selves perfect. - Swami Vivekananda