When I was considering what to do with my $10000 lottery winnings, my broker suggested that I invest half of it in gold, with a value that was...

I deposit half of my lottery winnings in gold which grows 8% per year.

Initial deposit `= 10000/2 = 5000`

Value after first year `= 5000xx1.08`

Value after two years `= (5000xx1.08)xx1.08 = 5000xx1.08^2`

So value after 10 years `= 5000xx1.08^10 = 10794.625`

I deposit half of my lottery winnings in CD's.

Initial deposit (present value) P = 5000

Compound interest i = 3%

compounding frequency n = 3month (quaterly)

Time t = 10 years

Using compound interest formula;

Future value `= P(1+i/n)^(nt)`

Future value

`= 5000(1+0.03/4)^(4xx10)`

`= 6741.743`

So my total earnings after 10 years `= 10794.625+6741.743 = 17536.37`

So my earnings after 10 years will be $17536.37