How do I solve this?
Rudy has been awarded some money in a settlement. He has the option to take a lump sum payment of $200,000 or get paid an annuity of $1,000 per month for the next 25 years. Which is the better deal for Rudy, and by how much, assuming the growth rate of the economy is 2.75% per year?

1)
Lump Sum: by $14,899.82

2)
Annuity: by $14,899.82

3)
Annuity: by $43,535.88

4)
Lump Sum: by $43,535.88

Hi there

First find the present value of annuity ordinary THE formula is
PVAO= pmt [(1-(1+r)^(-n))÷(r)]
PMT 1000×12months=12000 per year
R interest rate 0.0275
N time 25 years
So
PVAO=12,000×((1−(1+0.0275)^(
−25))÷(0.0275))
=214,899.82

Now compare the result with the amount of the lump sum
214,899.82−200,000
=14,899.82

So the answer is
2) Annuity: by $14,899.82

Hope it helps

Answer Link

chisnau chisnau · Answer 2 · 2019-06-14T13:26:51+02:00

Answer:

2) Annuity: by $14,899.82

Step-by-step explanation:

Given is -

Rudy has been awarded some money in a settlement.

He has the option to take a lump sum payment of $200,000

or get paid an annuity of $1,000 per month for the next 25 years.

Lets assume, that the growth rate of the economy is 2.75% per year

We will find how much the value becomes in annuity after 25 years.

p = [tex]12000\times12=12000[/tex]

r = 0.0275

n = 25 years

Present value formula is = [tex]p\frac{1-(1+r)^{-n} }{r}[/tex]

Putting the values in formula, we get

[tex]12000\frac{1-(1+0.0275)^{-25} }{0.0275}[/tex]

=>[tex]12000\frac{1-(1.0275)^{-25} }{0.0275}[/tex]

= $214900.36

Now the difference between annuity and lump sum =

[tex]214900.36-200000=14900.36[/tex]

We can take this as, close to given option 2.

Therefore, option 2 is correct.

The better deal for Rudy is to get paid an annuity, as it will give him $14899.82 more in 25 years than the lump sum amount.