The video introduces the time‑value‑of‑money concept as a tool for establishing equivalence between cash‑flow vectors, a principle that underlies everyday financial calculations such as loans, mortgages, and insurance premiums. Using a narrative featuring the superhero Mr. Incredible, the tutorial walks through a concrete example: borrowing €20,000 to buy a car and repaying it with four equal annual payments. It explains how to compute the present value of the loan amount and the series of repayments using a constant 3 % annual interest rate, derives the discount factors as negative powers of (1 + 0.03), and shows how to construct a payment vector in R. By dividing the loan amount by the present value of the payment vector, the required annual payment K is found to be approximately €5,380. The video emphasizes that the same cash‑flow equivalence approach will later be applied to insurance premium calculations and encourages viewers to practice with exercises before using online mortgage calculators.
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How can you use the time value of money concept for calculations that are relevant in everyday life? That's what you will learn in this video. You will meet a superhero and help him with his car loan. Off we go. Many of the transactions discussed in this course require you to establish an equivalence between two cash flow vectors. A first example is a loan or mortgage. For instance, to buy a house. In such an agreement, you receive a lump sum of cash from the bank, and in return, you pay back the capital with monthly payments. To calculate these monthly mortgage payments, you establish an equivalence relationship between the borrowed capital and the series of mortgage payments. A second example is an insurance product. Such a product requires an equivalence between the benefits covered by the insurance and a series of premium payments. To calculate these premiums later on in the course, you will use the exact same concept of equivalence between cash flow vectors. Please meet Mr. Incredible, an independent superhero living and working in Belgium. He needs a new car worth 20,000 Euro. Mr. Incredible wants to borrow this amount from the bank. He will pay back the loan with four yearly constant payments equal to, say, K. Mr. Incredible will pay his first loan payment at the end of the first year. The bank will determine an interest rate covering the interest the bank wishes to receive in return for the 20,000 Euro borrowed to our superhero. Can you calculate what the loan payment K should be? The cash flow from the bank to our superhero is very 20,000 at time zero, allowing Mr. Incredible to buy the car. The cash flow from the superhero to the bank is zero at time zero. Since his first loan payment is at the end of the first year, followed by 4 times k the repayments at times 1, 2, 3 and 4. So here is what you will. The present value of the cash flow from the bank to its client is very simple. That's just 20,000 Euro. To get the present value of the cash flow from the superhero to the bank, you discount each of the four loan payments at times 1, 2, 3 and 4. You require both present values to be equivalent and solve for the unknown K. Let's assume the bank charges a constant interest rate of 3% annually. The discount factors that you need should convert €1 at time 0 to 1, 2, 3 and 4 to the present moment. Hence, these factors are calculated as negative powers of 1 plus 0.03. You then create a vector payments in R that is 0 at time 0, followed by 4 times 1. If you multiply this vector with K, then you exactly get the cash flow vector from Mr. Incredible to the bank, as the timeline illustrates. Finally, you get the loan payment k by dividing 20,000 by the present value of the Vector payments with a rate of 3%, our superhero should annually pay 5,380 Euro to his bank over four years. With the first payment in one year from now. You are almost ready to challenge the many mortgage calculators available online. But first, let's get your hands dirty on some exercises.
