A retirement plan for Miss Cathleen

As a final assignment during her summer internship Cynthia is asked to do some calculations for Miss Cathleen. Miss Cathleen is a teacher, aged 40, who is planning for retirement. She wants to buy an annuity that provides her 18,000 EUR annually for life, beginning at age 65. Nothing is paid in case of death before 65. The figure below depicts the retirement plan for Miss Cathleen.

The one-year survival probabilities px are again preloaded.

This exercise is part of the course

Life Insurance Products Valuation in R

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Exercise instructions

Define kpx for a 40-year-old female.
Create discount_factors which discount payments at time zero (age 40) up to time length(kpx) - 1 at rate 3%.
Assign the pension payments to benefits. Make sure this vector has the same length as kpx.
Compute the single_premium as the sum of elementwise product of benefits, discount_factors and kpx. Print out the result.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Survival probabilities of (40)
kpx <- c(___, ___(px[(___):___])) 

# Discount factors (to age 40)
discount_factors <- (1 + ___) ^ -(0:(___))

# Pension benefits
benefits <- c(rep(___, ___), rep(___, length(kpx) - 25))

# The single premium
single_premium <- ___
single_premium

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