Question

Question 12 of 23 Question 12 e r 5 points Serv If you bought a car and you got an offer to pay for it an annual amount of 3000 starting year 4 for 4 years. Furthermore, you have to pay a one-time payment of 1000 at year 7. Find the equivalent Annual worth. (closest answer) 1798 2220 1627 2345

Answer 1

One time payment of 1000 at year 7

4 payments of 3000 from year 4 to year 7

PV of annual payment at the end of year 3 = A*(1-(1+r)^-n)/r

=3000*(1-(1+8%)^-4)/8%

=3000*(1-1.08^-4)/0.08

=3000*(1-0.735)/0.08

=3000*0.265/0.08

=9936.38

PV today =9936.38/(1+8%)^3 =9936.38/1.08^3=9936.38/1.2597 = 7887.82

PV of one time payment = 1000/(1+8%)^7 = 1000/1.08^7 = 1000/1.7138 = 583.49

Total PV = 7887.82+583.49 = 8471.31

Annual Cost will be given by, PV =A*(1-(1+r)^-n)/r

or, 8471.31 = A*(1-(1+8%)^-7)/8%

or, 8471.31 = A*(1-(1.08)^-7)/0.08

or, 8471.31 = A*(1-0.5835)/0.08

or, 8471.31 = A*0.4165/0.08

or, A = 8471.31 *0.08/0.4165

or, A = 1627.01

Hence third option is correct