Question

A perpetuity-immediate pays X per year. Kevin receives the first n payments, Jeffrey receives the next...

A perpetuity-immediate pays X per year. Kevin receives the first n payments, Jeffrey receives the next n payments and Hal receives the remaining payments. The present value of Kevin's payments is 20% of the present value of the original perpetuity. The present value of Hal's payments is K of the present value of the original perpetuity. Calculate the present value of Jeffrey's payments as a percentage of the original perpetuity.

Homework Answers

Answer #1

If r is the interest rate per year

PV of the perpetuity = X/r

PV of amount to Kevin = X/r* (1-1/(1+r)^n) = 20% of PV of original perpetuity

=> X/r*(1-1/(1+r)^n) = 0.2* X/r

=> (1-1/(1+r)^n) = 0.2 ....................... (1)

=> (1+r)^n =1.25 ............................. (2)

PV of amount to jeffrey = X/(1+r)^(n+1) + X/(1+r)^(n+2)+ .... + X/(1+r)^(n+n)

=1/(1+r)^n * (X/(1+r) + X/(1+r)^2+ .... +X/(1+r)^n )

=1/(1+r)^n * X/r*(1-1/(1+r)^n)

Putting the values from (1) and (2)

= 1/1.25 * X/r * 0.2

= 0.16* X/r

So, the % of PV of Jeffrey's payments to PV of original perpetuity =  0.16* X/r / (X/r) = 0.16 or 16%    

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-immediate makes the following pattern of payments every 3 years. It pays 3 at t...
A perpetuity-immediate makes the following pattern of payments every 3 years. It pays 3 at t = 1, then 1 at t = 2, then 4 at t = 3. In a list the payments are 3,1,4,3,1,4,3,1,4... and so on. Find the present value of this perpetuity assuming 8% effective interest per year.
The present value of an annual perpetuity immediate of 150 is equal to the present value...
The present value of an annual perpetuity immediate of 150 is equal to the present value of an annual perpetuity immediate that pays 100 at the end of the first 20 years and 200 at the end of year 21 and each year thereafter. Calculate i.
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...
A perpetuity pays $390.26 at the start of each year. The present value of this perpetuity...
A perpetuity pays $390.26 at the start of each year. The present value of this perpetuity at an annual effective interest rate i is equal to the present value of an annuity which pays 800 at the start of the first year, 790 at the start of the second year, 780 at the start of the third year and so on for 20 years. Find i to 1 significant figure.
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...
A 20 year annuity pays $2,250.00 per month. Payments are made at the end of each...
A 20 year annuity pays $2,250.00 per month. Payments are made at the end of each month. If the interest rate is 11% compounded monthly for the first 10 years, and 7% compounded monthly thereafter, what is the Present Value of annuity?
A 20-year annuity pays $2,250 per month, and payments are made at the end of each...
A 20-year annuity pays $2,250 per month, and payments are made at the end of each month. If the interest rate is 11 percent compounded monthly for the first ten years, and 7 percent compounded monthly thereafter, what is the present value of the annuity?
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....
An annuity-immediate has 20 annual payments starting at 5 and increasing by 10 every year. The...
An annuity-immediate has 20 annual payments starting at 5 and increasing by 10 every year. The annual effective rate of interest is 7%. Calculate the present value of this annuity. not a excel solution