##########
# R Loop #
##########

# Compute e

(1+1/1)^1
(1+1/2)^2
(1+1/4)^4
(1+1/1000)^1000

# while Loop
k = 1
while (k < 1001) {
cat("--------------------------", "\n")
cat("k is ", k, "\n")
cat("Compounded Interest is ", (1+1/k)^k, "\n")
k = k*10
}


# Simulate Pi
set.seed(12345)
k = 10
while (k < 100000001) {
point = cbind(runif(k, min = -1, max = 1),runif(k, min = -1, max = 1))
inside_circle = sum(((point[,1]^2+point[,2]^2)<1))
cat("--------------------------", "\n")
cat("Total number of points is ", k, "\n")
cat("magical number is ", inside_circle/k*4, "\n")
k = k*10
}

# Exercise on page 19
count = 0
i = 1
while (i<=n) {
if ((point[i,1]^2+point[i,2]^2)<1) {
count = count + 1
}
i = i + 1
}
count