We will study the return after 20 months of an investment by monthly installments at the monthly interest tax of 0.2%, knowing that a sum begins to give rise to interest the month following its deposit. More precisely, we consider a saver who deposits 100 euros per month into an account from n = 1 to n = 20.

We have: 1.002^19 = 1.039 || 1.002^20 = 1.041 || 1.002^21 = 1.043 || 1/0.002 = 500.

1) Explain how the final value of the investment is calculated in n = 2 and n = 3 and n = 4. Write the value obtained in n = 4 using the sum sign. 2) Generalize the previous result to give the expression of the final value of the investment at the end of the month 20 with the sum sign. 3) Calculate the final value of the investment by justifying the calculation steps. 4) Compare with the final value of an investment where the saver would have paid all the monthly payments at one time in n = 1. Explain the observed difference