The winner of a popular lottery is offered one of two options:

Question

i) a lump sum of $102 500
ii) $1000 every month for 10 years
If the money can be invested at 3.0% p/a, compounded monthly, which option should the winner choose? Justify your reasoning.

Every three months, Carlos deposits $400 in an account bearing 5.6% p/a, compounded quarterly. After 5 years, Carlos stops making regular deposits, but leaves the money in the account for another 2 years. How much money is in the account at the end of the 7 years?

Answer 1

first one:

find present value of second option ...
i = .03/12 = .0025
n = 120

PV = 1000( 1 - 1.025^-120)/.0025
= 103 561.75

So what do you think?

second one:

i = .056/4 = .01625
in 5 yrs, n = 20

amount after 5 years = 400(1.01625^20 - 1)/.01625
= 9364.179

invest that for 2 more years ----->
9364.179(1.01625)^8 = 10 653.06