Question

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 years, the payment is constant and equal to 10. Beginning in year 6, the payments start to increase. For year 6 and all future years, the current year’s payment is K% larger than the previous year’s payment. At an annual effective interest rate of 9.2%, the perpetuity has a present value of 167.50. Calculate K, given that K < 9.2.

The answer should be (4.00016).

Answer #1

1.

Present Value = 360/(0.013) + 40/(0.013)^{2}

Present Value = $264,378.70

2.

For First 5 years,

Present Value,

Using TVM calculation,

PV = [FV = 0, PMT = 10, T = 5, I = 9.20%]

PV = $38.7

so,

Present Value of Growing perpetual payment = 167.50 - 38.7 = $128.80

At the end of 5th year,

Value of perpetual payment = 128.80(1.092)^{5}

Value of perpetual payment = $200

Present Value of Growing Perpetuity = 10(1 + k)/(0.092 - k)

200(0.092 - k) = 10 + 10k

18.4 - 200k = 10 + 10k

**k = 4.00016%**

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, 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 semiannual payments with arithmetic
progression of 800, 750, 700, ..., 350, at i(2) =0.16. Find the
future value of this annuity 3 years after the last payment. Please
calculate it with steps, don't use the calculator with just an
answer only. thank you!

A perpetuity has a payment stream of Pt = 5t + 2 for t > 0 at
an annual effective interest rate of r. Another
perpetuity pays $40 continuously for the first year, $45
continuously for the second year, and so on, forever
with an annual effective interest rate of 5%. The present values of
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r.

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?

A perpetuity will make annual payments with the first payment
coming 9 years from now. The first payment is for $4700, and each
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Answer = $

ANSWER BOTH QUESTIONS PLEASE
1. A perpetuity-immediate makes a payment of an amount K every
three months. The present value of the perpetuity is $10,500.
Interest is at a nominal annual rate of 6% compounded semiannually.
In which of the following ranges is the amount K?
2. Deposits of $100 per month into an account start on January
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Find the...

A perpetuity will make payments of $100,000 every third year,
with the first payment occurring three years from now. The annual
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(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)

(1 pt) A perpetuity will make annual payments, with the first
payment coming 9 years from now. The first payment is for 4700
dollars and each payment that follows is 120 dollars more than the
one before. If the effective rate of interest is 5.2 percent, what
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Answer = dollars.

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will grow at the constant rate of 1.2% per annum, and where the
interest rate is 11% p.a., compounded semi-annually?

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