Question

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 annual effective rate of interest is 5%.

pls show all work written out without rounding until the last step

Answer #1

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. 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....

Find the present value of a 20-year annuity with annual payments
which pays $600 today and each subsequent payment is 5% greater
than the preceding payment. The annual effective rate of interest
is 10.25%.
Answer: 7851.19
Please show which equations you used and please do not use excel
to answer this question.

Which of the following statements is CORRECT?
a. The present value of a 3-year,
$150 annuity due will exceed the present value of a 3-year, $150
ordinary annuity.
b. An investment that has a nominal
rate of 6% with semiannual payments will have an effective rate
that is smaller than 6%.
c. If a loan has a nominal annual
rate of 8%, then the effective rate can never be greater than
8%.
d. The proportion of the payment
that goes...

Find the present value of an annuity due in perpetuity that pays
$75 at the beginning of each year for 20 years and increases by 4%
each year, starting at the beginning of the 21th year. Here assume
effective annual interest i = 7%.

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.

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...

Calculate the present value of annuity with payment of $1 at the
end of the first year and every two years thereafter. There are
total 5 payments. The last payment of $1 is at the end of 9th year.
The interest rate is 6% convertible semi-annually.(Write the
solution with formulas)

Find the Present value of an ANNUITY DUE (i.e. payments are at
the beginning of the period). It is 9 years, 8% and the payments
are $1,000.

What is the present value of an annuity due consisting of 5
annual payments of $4,000 with an interest rate of 9% p.a.
$16,959
$16,006
$19,558
$18,765
None of the above

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