Pension calculations ignoring mortality
Cynthia’s supervisor wants to stimulate her awareness of the time value of money and the use of survival probabilities in retirement calculations. He asks Cynthia to run some pension calculations - with and without taking mortality into account - for her own situation, that is a female living in Belgium, aged 20.
Cynthia comes up with a scenario in which her future employer pays her a pension from age 65 on until age 100. Her first yearly pension payment in this scenario equals 20,000 EUR and builds up each year with 2% (to offset inflation). Assume that the interest rate for the next 45 years is 3% and 4% thereafter.
What is the present value when mortality is not taken into account? Hence, you can assume that all 36 payments from age 65 until 100 are guaranteed.
This exercise is part of the course
Life Insurance Products Valuation in R
Exercise instructions
- Create
benefitswith the 36 pension payments starting at 20,000 at age 65 and increasing by 2% each year. - Define the
discount_factorsto discount these payments at rate 4% to age 65. - Compute the value at age 65 of the pension payments. Assign the result to
PV_65. - Discount
PV_65over a period of 45 years at rate 3% to obtain the present valuePV_20at age 20.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Pension benefits
benefits <- ___ * ___ ^ (___)
# Discount factors (to age 65)
discount_factors <- ___ ^ - (___)
# PV of pension at age 65
PV_65 <- ___(___ * ___)
PV_65
# PV of pension at age 20
PV_20 <- ___ * ___ ^ - ___
PV_20