Question

e. What is an annuity​ due? How does this differ from an ordinary​ annuity?

f. What is the present value of an ordinary annuity of

​$2 comma 6002,600

per year for

2525

years discounted back to the present at

1111

​percent? What would be the present value if it were an annuity​ due?

g. What is the future value of an ordinary annuity of

​$2 comma 6002,600

per year for

2525

years compounded at

1111

​percent? What would be the future value if it were an annuity​ due?

h. You have just borrowed

​$260 comma 000260,000​,

and you agree to pay it back over the next

3030

years in

3030

equal​ end-of-year payments plus

99

percent compound interest on the unpaid balance. What will be the size of these​ payments?

i. What is the present value of a perpetuity of

​$1 comma 8001,800

per year discounted back to the present at

66

​percent?

Answer 1

When payments are made/received at the beginning of each period, it is known as Annuity Due, while the payments are made/recieved at the end of each period in ordinary annuity

F.Present value of ordinary annuity = 2,600*PVAF(11%, 25 Years)

= 2,600*8.422

= $21,897.2

Annuity due = 2,600 + 2,600*PVAF(11%, 24 years)

= 2,600 + 2,600*8.348

=$24,304.8

G.Future value of ordinary annuity = 2,600*[{(1.11)^25 - 1}/0.11]

= 297,474.60

Annuity due = 297,474.60*1.11 = $330,196.80

H.size of payment = amount of loan/PVAF

= 260,000/PVAF(9%, 30 years)

= 260,000/10.2736

= $25,307.58

I.present value of perpetuity = amount/discount rate

= 1,800/6%

= $30,000