Question

vs

Answer 1

HI!!

Answer 2

for annual it is
\[A(t)=P_0(1+r)^t\] where \(r\) is the rate as a decimal and \(t\) is time (in years)

Answer 3

totally different formula for continuous compounding :
\[A(t)=P_0e^{rt}\]

Answer 4

Cont. Comp. Interest
Total = principal*e^(rate*years)
where 'e' = 2.718281828

Answer 5

yeah the difference is the formulas are different
if you compound more and more frequently say monthly, weekly, hourly etc and continue in this way, you will get the continuous compounding formula
you make more money that way too, although no one compounds interest continuously, it is for stuff found in nature

Answer 6

\[A=P_0(1+\frac{r}{n})^{nt} \\ \ \lim_{n \rightarrow \infty}A=\lim_{n \rightarrow \infty}P_0(1+\frac{r}{n})^{nt}=P_0e^{rt}\]

Answer 7

Here's a comparison

$1,000.00 at 7% interest for 2 years

annual Interest 1,144.90
cont comp int 1,150.27

Answer 8

okay