Calcute Return

Assume zero contribution at the beginning. We have the following parameters

• Annual return rate \(R\) (in percentage)

• Years \(Y\)

• Monthly contribution \(C\) (always contribute at the end of a month)

C = Constant

R = 6
Y = 30
C = 1000

For example, what’s the total amount in your retirement account at the end of month 1? It’s just \(C\) .

What’s the total amount in your retirement account at the end of month 2?

C * (1 + R/12/100) + C

Now write a function to return the total amount in your retirement account at the end of year \(Y\)

T = Y * 12
total = 0

for(i in 1:T)
  total = total * (1 + R/12/100) + C

total

To Do

• Write a function that can take \(R, Y, C\) as input and output total investment amount
• Fix \(Y\) and \(C\), vary \(R\) from 1% to 10% with an increase of 0.5%, i.e., you’ll try \(R\) being 1%, 1.5%, 2%, …, and go on. Try those \(R\) values and each will return you a total. Produce a plot of total vs \(R\)

Rvalues = seq(1, 10, by = 0.5) 
Rvalues
length(Rvalues)

Your code would look like this

# Continue with the definition of Rvalues above

m = length(Rvalues)
totals = rep(0, m)
for (t in 1:m){
  R = Rvalues[m]
  
  totals[m] = # your function
}

plot(Rvalues, totals) # check ggplot package

C = Contribution Rate

Now, we consider a case where the monthly contribution amount varies from year to year since it’s specified as a percentage of one’s monthly salary.

Your code would look like this

# m0 = initial salary
# c.rate = contribution rate
# a.rate = salary increase rate

# R = annual investment return rate 
# Y = service year

total  = 0
for(i in 1:Y){
  
#  current.m = salary in year t
#  current.C = contribution amount in year t
  
  for(j in 1:12){
# calculate total for each month
  }
}

total

[1] 0