Question

Marilyn has just won some money on a game show! She has the option to take a lump sum payment of $350,000 now or get paid an annuity of $3,200 at the beginning of each month for the next 10 years. Assuming the growth rate of the economy is 1.8% compounding annually over the next 10 years, which is the better deal for Marilyn and by how much?

Answer 1

@phi I know we keep working these out and I just do not think I am getting it.

Answer 2

The answers choices are

Lump Sum: by $4,842.99
Lump Sum: by $26,958.57
Annuity: by $4,842.99
Annuity: by $34,000

Answer 3

I know we have to do future value of the annuity - 350000 right?

Answer 4

What are your two different types of annuity equations ?

Answer 5

I think you use present value annuity due formula

Answer 6

I do not have equations because the book is wrong. It gives us the wrong equations so we are just supposed to use a calculator which I can do but i do not understand why we would use present and not future

Answer 7

She told me to use
http://easycalculation.com/mortgage/mortgage.php
to solve all the problems but I cannot get an answer still.

Answer 8

Here is what I came up with.

To compare the lump sum to the annuity we should compare present value to present value (or I suppose future value to future value... but we would need interest rates to do that). The present value of the lump sum is 350,000.

The present value of annuity due is
\[ PV= pymt \left(\frac{1}{i} - \frac{1}{i(1+i)^{nt-1} }+1\right ) \]
This formula almost matches yours, except we subtract 1 from the number of payments.

I finally got a number that matches one of your choices, but not at first,
I started by changing 1.8% to 0.018/12= 0.0015 per month. 12 payments per year * 10 years gives nt=120, so I used 119 in the formula. This did not match any of the choices.

Then I pondered this statement in the question
Assuming the growth rate of the economy is 1.8% **compounding annually**

Because I was compounding monthly, I decided I should try compounding *yearly*
I set i= 0.018, nt-1= 9 years (1 less than 10)
and a yearly payment of 12*3200= 38400

using those numbers, I get a PV of the annuity due as
354,842.99

that is exactly 4,842.99 more than the lump sum.
so I think the answer is Choice C: Annuity: by $4,842.99

Using your site
http://easycalculation.com/finance/pv-fv-annuitydue.php
with payment= 38400, i = 1.8%, number of periods = 10, it calculates the present value of annuity due as the same number up above: 354,842.99