C.S.JM. UNIVERSITY KANPUR Institute of business management:

C.S.JM. UNIVERSITY KANPUR Institute of business management Financial Mathematics Presentation on F.V. &F.V. OF Annuities Submitted To Anshul sir Submitted by Dheeraj kumar pandey Abhijeet kumar Abhishek dwivedi Aman upaddhyay Arpita vishnoi

FUTURE VALUE:

FUTURE VALUE A future value means that a given quantity of money today is worth more than what will be received at same point of time in the future . Conversely the future value of a given amount of money will always be greater then the present value of sum of the money invested at a rate of interest greater then zero. Future value is also known as terminal value.

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Once the investor has determined his interest rate,say,10 % ,he would like to receive at least Rs.1.10 after one year or 110 % of the original investment of Rs. 1 today a two year period is two successive one year period. When the investor invested Rs .1 for one year . he must have received Rs 1.10 back at the end of one year in exchang for the original Rs 1.if the investor would expect 110% of that amount ,at the end of the second year . notice that for any time after the first year, he will insist on the receiving interest on the first year’s interest as well as interest on the original amount. Compound interest is the interest that is received on the original amount as well as on any interest earned but not withdrawn during earlier periods .

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compounding is the process of finding the future value of cash flow by applying the concept of compound interest . simple interest is the interest that is calculated only on the original amount and thus ,no compounding of interest takes place .

FVn = PV (1+r)n :

FVn = PV (1+r) n Here , FVn = future value of initial cash flow n years hence. PV = initial cash flow(present value in sum today). r = annual rate of interest per rupee [R/100] n = number of year

EXAMPLE- Under a particular sceme, Rs. 1,000 was invested for 3 years at 8% p.a.compounded half -yearly. Find out the future value. :

EXAMPLE- Under a particular sceme , Rs. 1,000 was invested for 3 years at 8% p.a.compounded half -yearly. Find out the future value. PV = 1,000, r = 8 / 100 * 2 = 0.04 n = 3 * 2 = 6 FV n = PV ( 1 + r ) n FV 3 = 1,000 (1 + 0.O4) 6 or FV 3 = 1,000 (1.04) 6 FV 3 = 1,000 * 1.27 = Rs. 1,270

FUTURE VALUE OF AN ANNUITY:

FUTURE VALUE OF AN ANNUITY Annuity is a fixed payment each year for a specified number of years if you rent a flat and promise to make a series of payment over an agreed period . you have created an annuity . the equal instalments loans from the house financing companies or employers are common example of annuities .

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Suppose a constant sum of Rs 1 is deposited in a saving account at the end of the each year for four years at the 6 % interest . this implies that Rs 1 deposited at the end of the first year .will grow for 3 years , Rs. 1at the end of the second year for two years ,Rs 1 at the end of the third year for one year and Rs 1 at the end of the fourth year will not yield any interest . using of the concept of the compound value of a lump sum , we can compute the value of annuity .

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P1 = a [ (1+r) n – 1 / r ] Here, P1 = Future value or total amount a = Ordinary annuity value r = Rate of interest per rupee per period n = period

An annuity consists of 8 annual payments of Rs. 1,500 each, the first being made at theend of 5 years. Find out the amount (future value) of this annuity if money is worth 6% p.a compounded annually. :

An annuity consists of 8 annual payments of Rs. 1,500 each, the first being made at theend of 5 years. Find out the amount (future value) of this annuity if money is worth 6% p.a compounded annually. P 1 = a/r {( 1 + n) n – 1} P 1 = 1,500 / 0.06{(1 + 0.06) 8 -1} or P 1 = 1500 / 0.06 {( log 1.06 * 8) -1} or P 1 = 25,OOO {Antilog 0.2024 – 1} or P 1 = 25,000 {1.594 – 1} P 1 = 25,000 * 0.594 = Rs. 14,850 Hence, the future value of deferred annuity is Rs. 14,850.

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