Question

Manuel just won the lottery and the prize was $ 1 million. You have the option of receiving a lump sum of $ 312,950 or $ 50,000 per year for the next 20 years. If Miguel can invest the single amount at 9% or invest the annual payments at 7%; Which one should I choose?

a. one-time amount of 312,950

b. b. annual payments of 50,000

Answer 1

Future value of these payments after 20 years.

Part 1:

Future Value:

Future Value is Value of current asset at future date grown at given int rate or growth rate.

FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Present Value	$       312,950.00
Int Rate	9.0000%
Periods	20

Future Value = Present Value * ( 1 + r )^n
= $ 312950 ( 1 + 0.09) ^ 20
= $ 312950 ( 1.09 ^ 20)
= $ 312950 * 5.6044
= $ 1753900.35

Part 2:

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$          50,000.00
Int Rate	7.000%
Periods	20

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 50000 * [ [ ( 1 + 0.07 ) ^ 20 ] - 1 ] / 0.07
= $ 50000 * [ [ ( 1.07 ) ^ 20 ] - 1 ] / 0.07
= $ 50000 * [ [3.8697] - 1 ] / 0.07
= $ 50000 * [2.8697] /0.07
= $ 2049774.62

Hence Annuity of $ 50000 for 20 years is choosen as it has higher Future value after 20 Years.