Question

7. The equivalent annual w $135,578. If the cash flow in $20.000. what is the value of annual worth of an increasing arithmetie gradient is cash now in year is $30.000 and the gradient amount is value of at an interest rate of 10% per year? [15 marks) G

Answer 1

Equivalent annual worth=$135578

Initial Cash flow=$30000
Gradiant amount=$20000

Equivalent annual worth=Present worth*Present Annuity factor

=30000/(1.1)+50000/(1.1)^2+70000/(1.1)^3+...

=30000(P/A,10%,n)+20000(P/G,10%,n)

135578=30000(P/A,10%,n)+20000(P/G,10%,n)

We are referring compound interest factors under i=10% for (P/A and P/G ) ratios

when n=3 P/A,10%,3=2.487 and P/G,10%,3=2.329

Present Worth=121190

when n=4 P/A,10%,4=3.170 and P/G,10%,4=4.378

Present Worth =182660

Hence 3<n<4

therefore n=3.295 years

Present Worth formula =Annuity*Present annuity factor

Arithmatic gradiant formula =(P/G,r%,n)=(1+i)^N-i*N-1/(i^2(1+i)^N)

Answer is 3.295 years