Which is the better deal 10000 invested at 5 compounded year

Which is the better deal, $10,000 invested at 5%, compounded yearly, for 20 years, or $5,000 invested at 10%, compounded continuously, for 20 years?

Solution

$10,000 invested at 5%, compounded yearly, for 20 years
compound interest formula: A=P(1+i)^n, P=initial investment, i=interest rate per compounding period, n=number of periods, A=amt after n-periods
For given problem:
P=$10000
i=.05
n=20
A=10000(1+.05)^20
A=10000(1.05)^20$26,533

$5,000 invested at 10%, compounded continuously, for 20 years
Formula for continuous compounding: A=Pe^rt, P=initial investment, r=interest rate, t=number of years, A=amt after t-years
For given problem:
P=$5000
r=0.10
t=20
A=amt after t-years
A=5000*e^.10*20
A=5000*e^2
A$36,945

$5000 investment compounded continuously is the better dea