Saving for university

Cynthia's parents anticipate her graduation from high school and start saving money to finance her studies. For each study year at a Belgian university, they will need 3500 EUR.

In the timeline printed below, the red cash flows denote the saving deposits by Cynthia's parents and the blue cash flows denote the study expenses.

Assume a constant interest rate of 3%. Can you compute the value of the savings amount \(K\) using the notion of actuarial equivalence of cash flows?

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Life Insurance Products Valuation in R

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练习说明

Define the discount_factors at times 0 through 9 for the assumed interest rate of 3%.
Create the vector deposits, representing the deposit pattern corresponding to all 10 time points. Since deposits are only made at time points 1 to 4, the vector deposits should start with a 0, then four times a 1 and then 5 times 0 again.
Define payments, representing the expenses at the university. This vector should contain 0 five times, followed by 3500 (five times, again).

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通过完成这段示例代码来试试这个练习。

# Define the discount factors
discount_factors <- (___ + ___) ^ - (___)

# Define the deposit pattern
deposits <- c(___, ___(___, ___), ___(___, ___))

# Define the university expenses
payments <- c(___(___, ___), ___(___, ___))

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