Question

A perpetuity has payments of 1, 2, 1, 3, 1, 4, 1, 5, ..... Payments are...

A perpetuity has payments of 1, 2, 1, 3, 1, 4, 1, 5, ..... Payments are made at the end of each year. You may assume an annual effective interest rate of 5%. Determine the present value of the perpetuity.

Please give a detailed calculation process, instead of table.

Thank you.

Homework Answers

Answer #1

solution:

PV of the payments of 1 at time 1,3,5,... is

   = v+(v3)+(v5)+...

= v/(1-(v^2))

= 9.76
PV of payments of 2,3,4,...,at time 2,4,6,... candetermined by increasing annuity at effective rate

j=1.052 for a 2-year period.
So the PV of the increasing payments is
=(2/j)+(1/(j2)) = 19.51 + 95.18

= 114.69

PV of the total perpetuity = 114.69 + 9.76

= 124.45

Here the PV given (114.69) is as of t=1, not t=0.

so the solution is

=9.76 + (19.51 + 95.18)(1.05^-1)

= 118.94

ThankYou.....


Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A perpetuity has payments of 1, 2, 3, ...., 98, 99, 100, 99, 98, 97, 96,...
A perpetuity has payments of 1, 2, 3, ...., 98, 99, 100, 99, 98, 97, 96, ...., 3, 2, 1, 2, 3, 4, ...., 99, 100, 99, 98, ....., 3, 2, 1, 2, ...., 99, 100, 99, 98, ...., 3, ,2, 1.... If the payments are made annually, and the annual effective interest rate is 7%, Find the value of the perpetuity at the time of the first payment. Please give detailed calculation process, Thank you!
A perpetuity with payments of 1 at the end of each year has a present value...
A perpetuity with payments of 1 at the end of each year has a present value of 40. A 10-year annuity pays X at the beginning of each year. Assuming the same effective interest rate, the present values of the perpetuity and the 10-year annuity are equal. Find X.
Perpetuity X has annual payments of 1,2,3,... at the end of each year. Perpetuity Y has...
Perpetuity X has annual payments of 1,2,3,... at the end of each year. Perpetuity Y has annual payments of q, q, 2q, 2q, 3q, 3q, ... at the end of each year. The present value of X is equal to the present value of Y at an annual effective interest rate of 10%. Calculate q. I'm new to perpetuities but basically understand how perpetuities work. I also have a formula for perpetuities that increase every year. I just can't figure...
1. A perpetuity-due has monthly payments in this pattern: Q, 2Q, 3Q, Q, 2Q, 3Q, Q,...
1. A perpetuity-due has monthly payments in this pattern: Q, 2Q, 3Q, Q, 2Q, 3Q, Q, 2Q, 3Q, . . . The present value of the perpetuity is $700,000 and the effective annual discount rate is 6%. Find Q. 2. A 30 year annuity-immediate has first payment $1200 and each subsequent payment increases by 0.5%. The payments are monthly and the annual effective rate is 8%. Find the accumulated value of the annuity at the end of 30 years. 3....
A perpetuity with an annual payment of $1,000 (payments start N years from today) has a...
A perpetuity with an annual payment of $1,000 (payments start N years from today) has a present value (today) of $6,830. A second perpetuity, which will begin five years after the first perpetuity begins, has a present value of $8,482. The annual interest rate is 10 percent. Determine the value of each payment of the second perpetuity?
An investor buys a perpetuity-immediate providing annual payments of 1, with an annual effective interest rate...
An investor buys a perpetuity-immediate providing annual payments of 1, with an annual effective interest rate of i and Macaulay duration of 17.6 years. Calculate the Macaulay duration in years using an annual effective interest rate of 2i instead of i.
You are given a perpetuity that makes payments every two years, with a payment at the...
You are given a perpetuity that makes payments every two years, with a payment at the beginning of the year numbered 2n + 1, for n = 0, 1, 2, …, equal to 1/((n+1)(n+2)*3n). Find the present value of this perpetuity at time 0, given that the annual effective interest rate is 4.5%.  
Find the present value of an annuity in perpetuity that makes payments of $70 at the...
Find the present value of an annuity in perpetuity that makes payments of $70 at the end of year 6, year 12, year 18, year 24, etc. and makes payments of $60 at the end of year 1, year 4, year 7, year 10, etc. and where effective annual interest is i = 7%.
1. Perpetuities in arithmetic progression. If a perpetuity has first payment P and each payment increases...
1. Perpetuities in arithmetic progression. If a perpetuity has first payment P and each payment increases by Q, then its present value, one period before the first payment, is P/i + Q/i^2 Using this formula, find the present value of a perpetuity-immediate which has annual payments with first payment $360 and each subsequent payment increasing by $40, at annual interest rate 1.3%. The answer should be ($264,378.70). 2. Filip buys a perpetuity-immediate with varying annual payments. During the first 5...
1. Find the present value of a 30-year annuity-due with semiannual payments in which the first...
1. Find the present value of a 30-year annuity-due with semiannual payments in which the first payment is $20,000, the second payment is $21,600, the third payment is $23,328, the fourth payment is $25,194.24, etc., assuming an annual effective rate of interest of 16%. 2. Find the present value of a varying perpetuity-DUE in which payments are made every two years with the first payment being $245, and each payment thereafter is $150 larger than the previous payment. Assume the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT