R Notebook

# Code Created by Paras Takkar
# Problem 1

solve_interest_rate <- function(x, t) {
  i <- x^(1/t) - 1
  return(i)
}

# Test the function with x = 5 and t = 15
x <- 5
t <- 15

rate <- solve_interest_rate(x, t)

cat("Interest rate:", rate, "\n")

Interest rate: 0.1132636 

# Verify by hand using k = 1000
k <- 1000
accumulated_value <- k * (1 + rate)^t

cat("Accumulated value of $1,000 after 15 years:", accumulated_value, "\n")

Accumulated value of $1,000 after 15 years: 5000 

# Code Created by Paras Takkar
# Problem 2
t <- as.Date(c("2024-01-01",
               "2024-02-01",
               "2024-04-01",
               "2024-06-01",
               "2024-08-01",
               "2024-10-01",
               "2024-11-01",
               "2024-12-31"))

B_t <- c(200000,
         205000,
         211000,
         214000,
         219000,
         225000,
         225500,
         231000)

W_t <- c(0,
         10000,
         -2000,
         -1500,
         4000,
         3500,
         1500,
         0)

df <- data.frame(t, B_t, W_t)

B_t_minus_1 <- c(NA, B_t[-length(B_t)])

B_before_flow <- B_t - W_t

r_t <- (B_before_flow / B_t_minus_1) - 1

df$B_t_minus_1 <- B_t_minus_1
df$r_t <- r_t

twrr_2024 <- prod(1 + r_t[-1]) - 1

df

cat("TWRR (decimal form):", twrr_2024, "\n")

TWRR (decimal form): 0.07221138 

cat("TWRR expressed as a percentage:", 100 * twrr_2024, "%\n")

TWRR expressed as a percentage: 7.221138 %