a For year 1, the value of the investment to the investor a(what he starts with)+( the interest on what he starts With ￡100+10%X100=￡100(1+10%)=￡110 o to--10%->t1 100->100+10%of100 =100(1+10%) =2110
◼ For year 1, the value of the investment to the investor: ❑ (what he starts with) + (the interest on what he starts with) ❑ £100 + 10%x£100 = £100(1+10%) = £110 ❑ t0—10%—>t1 100 —> 100+10% of 100 = 100(1+10%) =£110
For year 2, the value of the investment to the investor, a what he starts with at the beginning of year 2)+(the interest earned over year 2) ￡110+10%X110=￡110(1+10%)=￡121 10%—>t-10%—>t2 100→>100+10%X00 =100(1+10%) 110 >110+10%X|10 =1101+10%) =2121 a110(1+10%)=100(+109%)(+10%) =100(+10%)2 =￡121
◼ For year 2, the value of the investment to the investor: ❑ (what he starts with at the beginning of year 2) + (the interest earned over year 2) ❑ £110 +10%x£l 10 = £110(1+10%) = £121 t0 —10% —> t1 —10% —> t2 100 —> 100+10%xl00 =100(1+10%) =110 —> 110+10%x l10 = 110(1+10%) =£121 ❑ 110(1+10%) = 100(l+10%)(l+10%) = 100(l+10%)2 = £121
For year 3 the value of the investment to the investor ato-10%>t1-10%—>t2-10%>t 100 >100+10%X00 =1001+10%) =110->110+10%X0 =1101+10%) =100(1+10%)2 =121>121+10%X21 121(1+10%) =100(+10%)3 =2133.1
◼ For year 3, the value of the investment to the investor: ❑ t0 —10%—> t1 —10%—> t2 —10%—> t3 100 —> 100+10%xl00 =100(1+10%) = 110 —> 110+10%xll0 = 110(1+10%) =100(1+10%)2 =121 —> 121+10%xl21 =121(1+10%) =100(l+10%)3 =£133.1
a The value of the investment at different time periods can be summarised as follows >t -->t 100100+10%)1100(+10%)2100(+10%) For year n, General compounding idea as follows a For a given initial lump sum A a For a given term of investment n a For a given rate of interest 1% a Future value(Fv of the investment is given by a FV=A(+i%)n
◼ The value of the investment at different time periods can be summarised as follows: ❑ t0 ----------> t1 -------------> t2 -------------> t3 100 100(l+10%)1 100(l+10%)2 100(l+10%)3 ◼ For year n, General compounding idea as follows: ❑ For a given initial lump sum A ❑ For a given term of investment n ❑ For a given rate of interest i% ❑ Future value (FV) of the investment is given by: ❑ FV = A(l+i%)n
DISCOUNTING Discounting is the reverse side of the coin to compounding With discounting the time direction is reversed For the value of a sum of money in the future, we want to know what this future sum is worth to us right now Considering the position of a money lender, Aclient would like to borrow some money in order to finance some immediate expenditure however the client does have an asset that will be available, not to-day, but in 1 years time. At this time the asset will have a value of f100. thus the client has an asset -E100 available in one years time-but unfortunately for him he wants money NoW The client can thus pose the following question to the money lender
DISCOUNTING ◼ Discounting is the reverse side of the coin to compounding ◼ With discounting the time direction is reversed. ◼ For the value of a sum of money in the future, we want to know what this future sum is worth to us right now. ◼ Considering the position of a money lender, A client would like to borrow some money in order to finance some immediate expenditure, however the client does have an asset that will be available , not to-day, but in 1 years time. At this time the asset will have a value of £100. Thus the client has an asset - £100 available in one years time -but unfortunately for him he wants money NOW. The client can thus pose the following question to the money lender: