Question

Kylie would like to purchase a perpetuity paying 400 per year, with the first payment due at the end of year 14. The following 2 purchase options are equivalent using an effective annual valuation interest rate of i

. • Option 1: Paying 75 at the end of each year for 13 years.

• Option 2: Paying K at the end of the year for the first five years (and paying nothing after that).

Calculate K.

Answer #1

Danielle wants to purchase a perpetuity paying 2000 per year
where the first payment will be at the end of year 11. She can
purchase it by either: a. Paying 1900 per year at the end of each
year for 10 years; or b. Paying K per year at the end of each year
for the first 5 years and nothing for the next 5 years. Use part a.
to find i and then part b to find K

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. 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 paying 50 at the end of each year forever starting 6
years from now using an annual effective rate of interest of
10%.

Jones purchased a perpetuity today for $7, 000. He will receive
the first annual payment of $200 five years from now. The second
annual payment will be $200 plus an amount C. Each subsequent
payment will be the prior payment plus an additional constant
amount C. If the effective annual interest rate is 4%, find C. I
know the answer is 5.1 but I'm not sure how to get there.

Perpetuity A pays $0.50 per year, but its 1st payment will be in
1 year from today. Perpetuity B pays $1 every two years, and its
1st payment will be in 2 years from today. Which perpetuity will
you choose if the annual interest rate is 5%?
(a). A
(b). B
(c). They are of same value

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...

ANSWER THE FOLLOWING:
A)A sequence of quarterly payments o P6,267 each, with the first
payment due at the end of 2 years and the last payment at the end
of 13 years. Find the present worth of these payments if money is
worth 5% compounded quarterly.
B)A manufacture borrows P2,211,340 with interest at 6%
compounded monthly, and agrees to discharge the loan by a sequence
of equal monthly payments for 4 years with the first payment at the
beginning of...

A)A sequence of quarterly payments o P6,267 each, with the first
payment due at the end of 2 years and the last payment at the end
of 13 years. Find the present worth of these payments if money is
worth 5% compounded quarterly.
B)A manufacture borrows P2,211,340 with interest at 6%
compounded monthly, and agrees to discharge the loan by a sequence
of equal monthly payments for 4 years with the first payment at the
beginning of the 4th year. Find...

A perpetuity will make payments of $100,000 every third year,
with the first payment occurring three years from now. The annual
nominal interest rate convertible quarterly is 8%. Find the present
value of this perpetuity.
(I did this problem, just want to check if I did it correctly
because the answer doesn't look right to me, not sure what I did
incorrectly, I got PV = 372,800.47)

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