Let it be a constant annuity of n payments and rate be r
PV=C/(1+r)+C*(1+g)/(1+r)^2+C*(1+g)^2/(1+r)^3...C*(1+g)^(n-1)/(1+r)^n
As this is a geometric progression with first term(a) as C/(1+r) and common ratio(d) as (1+g)/(1+r) and number of terms(x) as n
Sum becomes=a*(1-d^x)/(1-d)=C/(1+r)*(1-((1+g)/(1+r))^n)/(1-(1+g)/(1+r))=C/(r-g)*(1-((1+g)/(1+r))^n)
When g=r, PV=n*C/(1+r)
Implications: there is no effect of growth
Q4 Derive the formula for the PV of an n- annual payment annuity with growth at...
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orla 7.2 S-P+I armla 7.34S-P(I +) restated as FV-PV( 1 + ir Fermula S2 Farmals 10.1--1 Formula 11. FV er year 1+i-1 Formula 12.1P-1 Finding the fatare vaie et an ordisary general annuity using the eflective rate of inter est per paryment peried where p ( +i-1 PVr = PMT[I-(1+p)""I Finding the present value of an ordinary general annuity uning the eflective rate ot interest per paymeet period Farmata 12.3 Formula 124 SIZE OF THE NTH PAYMENT Finding the sire...
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