Question

you want to buy an ordinary annuity that will pay you 4000 a year for next 20 years . you expect annual interest rate will be 8 percent over that time period . the maximum price you would be willing to pay for annuity is closest to ​

Answer 1

Given,

Principle =$4000

Time =20 years

Rate =8% p.a.

We know,

SI =PRT/100

.'. SI =$(4000×20×8/100)

=$6400

Now,

Amount = SI + Principle

=$(6400+4000)

=$10400

.'. THE MAXIMUM PRICE YOU WOULD BE WILLING TO PAY FOR ANNUITY TO $10400

Answer 2

The maximum price that I would pay for this annuity is $39,272.59.

Step-by-step explanation:

Given: You want to buy an ordinary annuity that will pay you 4000 a year for the next 20 years.

The interest rate will be 8 percent over that time period.

To find: The maximum price you would be willing to pay for the annuity.

Ordinary Annuity:

An ordinary annuity is a type of annuity that pays out at the conclusion of each term.

An annuity provides investors with equal payouts on a regular basis. The investment period is specified and limited.

Solution:

The purchase price is equivalent to the present value of expected cash flows, as calculated below:

$PV_{oa} = A * \frac{1-(1+r)^{-n} }{r}$

$PV_{oa} = \ 4000*$$\frac{1-(1+0.08)^{-20} }{0.08}$

$PV_{oa} = \ 4000*$$9.8181474$

$PV_{oa} = \ 39,272.59$

Where,

$PV_{oa} =$ Present Value of ordinary annuity

A = Amount of annuity payment

r= interest rate

n= number of time periods

Hence, the maximum price that I would pay for this annuity is $39,272.59.