Monthly mortgage loan payments
Cynthia's parents receive a loan of 125,000 EUR in return for fixed monthly payments \(K\) over the next 20 years as visualized in the graph below.
Using the variables number_payments
and monthly_interest
defined in the previous exercise, which are preloaded for you, it's up to you to determine the value of \(K\) based on the principle of actuarial equivalence.
This exercise is part of the course
Life Insurance Products Valuation in R
Exercise instructions
- Define the discount factors corresponding to the first payment month up until the last payment month. Do this by raising 1 plus
monthly_interest
to the power minus a vector from 1 untilnumber_payments
. - Create the variable
payments
which reflects the payment pattern. This should be a vector of ones with lengthnumber_payments
. - Finally, calculate the monthly payment \(K\) by dividing the mortgage amount 125,000 by the present value of the payment pattern.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Define the discount factors
discount_factors <- (___) ^ - (___)
# Define the payment pattern
payments <- rep(___, ___)
# Calculate the monthly loan payment K
K <- ___ / ___(___ * ___)
K