a How much will you be prepared to lend me right now given that I can pay you back f100 in one year time? For money lender, it's a compounding problem for 1 year, which can be represented as at-10%—>t1 ?(1+10%)=100 ?=100/(1+10%)=90.91 o E90.91 is called the discounted value or the present value(Pv of f100 in 1 year
❑ How much will you be prepared to lend me right now given that I can pay you back £100 in one year time? ◼ For money lender, it’s a compounding problem for 1 year, which can be represented as: ❑ t0—10%—>t1 ? —> ?(1+10%) =100 ?=100/(1+10%) =£90.91 ❑ £90.91 is called the discounted value or the present value (PV) of £100 in 1 year
a The inverse relationship between the present value of a future sum of money and the going rate of interest If the interest rate increases the denominator in the expression for increases, and results in a fall in the pv If the rate of interest falls the denominator falls, and results in the Pv of a future sum of money will rise a For 2 years, t2 ?(+10%)2=100 ?=100/(1+10%)2=￡8265
❑ The inverse relationship between the present value of a future sum of money and the going rate of interest ◼ If the interest rate increases, the denominator in the expression for ? increases, and results in a fall in the PV. ◼ If the rate of interest falls, the denominator falls , and results in the PV of a future sum of money will rise. ❑ For 2 years, ◼ t0 ------> t1-----> t2 ?-----------------> ?(l+10%)2 = 100 ?=100/(1+10%)2 = £82.65
ato<-109%—t1<-10%—t2 90.91<-100 82.65< 100 ￡100in1 year is worth￡90.91to-day ￡100in2 years is worth￡8265to-day General rule for discounting can be represented as follows 0 t1 100/(+10%)1<--100 100/(+10%)2 100 uFor3yea,PV=100/(+10%)3 a For 4 year, PV = 100/(1+10%)4
❑ t0 <—10%— t1 <—10%—t2 90.91 < --- 100 82.65 < --------------------100 ◼ £100 in 1 year is worth £90.91 to-day ◼ £100 in 2 years is worth £82.65 to-day. ◼ General rule for discounting can be represented as follows: ❑ t0 < --------------------t1 < --------------t2 100 /(l+10%)1 <---- 100 100 / (l+10%)2 < ----------------------100 ❑ For 3 year, PV = 100/(l+10%)3 ❑ For 4 year, PV = 100/(l+10%)4