Deposits of the saving plan
Now that you have defined the variables discount_factors, deposits and payments, you are ready to determine the value \(K\) of the yearly savings deposits using the actuarial equivalence relationship between the deposits (red cash flow) and the payments (blue cash flow).
This exercise is part of the course
Life Insurance Products Valuation in R
Exercise instructions
- Calculate the present value of the deposit pattern as the
sum()of the elementwise product ofdepositsanddiscount_factors. - Do the same for the payment pattern by summing over the product of
paymentsanddiscount_factors. - Using the concept of actuarial equivalence, the yearly deposit
Kin the first four years can be calculated by dividingPV_paymentbyPV_deposit.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Calculate the present value of the deposits
PV_deposit <- ___(___ * ___)
# Calculate the present value of the payments
PV_payment <- ___(___ * ___)
# Calculate the yearly deposit K in the first 4 years
K <- ___
K