# Loan Rate Calculator

# The annuity payment formula is given by:

# A = P * (i + i / ( (1 + i) ^ n - 1) )

# where A = periodic payment amount, P = amount of principle net of initial payments (subtract down-payments)

# i = periodic interest rate, n = total number of payments

# Part 1. Write a function that takes as input - amount of principle (p), down-payment (dp), interest rate (i),

# number of years in loan (y) - and return the monthly payment for the loan. annutity_payment <- function(p, dp, i, y) { annutity <- return(annutity) }

# Part 2. Using your annutity_payment function write a function that calculates the total amount payed. total_payed <- function(p, dp, i, y){ total <- return(total) }

# Part 3. Now using your functions evaluate which of these loans result in you paying the least amount:

# a - Principal = 200,000, Down Payment = 20,500, APR = 4.5%, Length of Loan = 30 years.

# b - Principal = 200,000, Down Payment = 30,000, APR = 5.0%, Length of Loan = 15 years.

# c - Principal = 200,000, Down Payment = 30,000, APR = 4.5%, Length of Loan = 30 years.

# d - Principal = 200,000, Down Payment = 50,000, APR = 5.0%, Length of Loan = 15 years.

# e - Principal = 200,000, Down Payment = 50,000, APR = 6.0%, Length of Loan = 15 years.

# f - Principal = 200,000, Down Payment = 20,500, APR = 5.0%, Length of Loan = 30 years.

# Part 4. Why might someone take a less than optimal option?

# Part 5. Now suppose instead of a fixed rate mortgage you are looking to get an adjustable rate mortgage (ARM).

# The starting rate is guaranteed at 3% APR for the first five years but then will increase by 1.5% every 60 months

# The principal amount is 200,000 and your down payment is 20,000. The total length of the loan is 15 years.

# # What will the total cost of your mortgage be?

# # HINT: You may want to write a function that computes the balance paid after X months using this formula.

# Balance Paid = (12 * monthly payment / annual interest rate)((1 + annual interest rate/12) ^ number of months paid - 1)

(((THIS NEEDS TO BE SOLVED BY R STUDIO)))