Question

Help anyone, please?

Rehan has been awarded some money in a settlement. He has the option to take a lump sum payment of $170,000 or get paid an annuity of $1,000 per month for the next 20 years. Which is the better deal for Rehan, and by how much, assuming the growth rate of the economy is 3.05% per year?

Lump Sum: by $63,712.66

Lump Sum: by $7,707.19

Annuity: by $63,712.66

Annuity: by $7,707.19

Answer 1

i think it's the 1st one?

Answer 2

could you show me step by step?

Answer 3

@Kainui help please?

Answer 4

You need the formula for the present value of an annuity.

Answer 5

\( P = A \times \dfrac{1 - (1 + i)^{-n}}{i} \)

where P = present value
A = annualized payment (per period)
i = interest rate per period expressed as a decimal
n = number of periods

\( P = $1,000 \times \dfrac{1 - (1 + \frac{0.0305}{12})^{-{240}}}{\frac{0.0305}{12}} \)

\(P = $179,499.73\)

The present value of the annuity is higher than $170,000, but not by the amount in your choices. Is all the given info correct in your problem?

Answer 6

Yes its all correct :/

Answer 7

The difference is $9,499.73, not $7,707.19. I don't understand how your choices have that amount.

Answer 8

@mathstudent55 :(