Question

Billy is oﬀered two payment plans. One is a perpetuity-immediate paying $1000 every year at 10% eﬀective interest per year. The other is an annuity-immediate paying $1450 every year at 8% per year for 10 years, plus an extra $500 with the 5th payment. Which payment plan has a larger present value?

Answer #1

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 values of the following three annuities are equal:
(i) perpetuity-immediate paying 1 each year, calculated at an
annual effective interest rate of 7.84%. (ii) 26-year
annuity-immediate paying 1 each year, calculated at an annual
effective interest rate of j%. (iii) n-year annuity-immediate
paying 1 each year, calculated at an annual effective interest rate
of (j−1)%. Calculate n.

A 10-year annuity immediate has a ﬁrst payment of X. The payment
increases by 100 each year for 5 times and stays level afterwards.
Under an eﬀective annual rate of 6.5%, the present value of this
annuity is 3733.2264. Calculate X。 please calculate it with step,
don't use financial calculate with direct answer. Will rate it,
thx:)

Nara inherits a perpetuity from her grandfather that will pay
here $3000 today and every year forever. The annual interest rate
is 4%.
a) How much is Nara's inheritance worth? Nara decides to sell
the perpetuity (for its present value) and instead buy an annuity
due paying $P for the next 28 years.
b) What is $P? She changes her mind again, and decides instead
on an annuity due paying $6000 per year for n years, except for the
last...

Nara inherits a perpetuity from her grandfather that will pay
here $4000 today and every year forever. The annual interest rate
is 6%.
a) How much is Nara's inheritance worth? Nara decides to sell
the perpetuity (for its present value) and instead buy an annuity
due paying $P for the next 24 years.
b) What is $P? She changes her mind again, and decides instead
on an annuity due paying $8000 per year for n years, except for the
last...

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
1, 2015 and continue through December 1, 2034. The account earn a
nominal annual interest rate of 6% compounded quarterly.
Find the...

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...

An annuity immediate pays 200 every month for 10 years.
Calculate the present value at the following rates of interest:
Annual effective interest rate of 6%
Nominal interest rate convertible monthly of 8%
Nominal rate of discount convertible once every two years of
4%

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

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%.

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