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A person saves €1 in the first month and decides to double the amount he saves the next month. He continues this pattern of saving twice the amount he saved the previous month for 12 months how much will he save on the 12th month and how much will he have saved in total for the year ignoring any interest he received?

Respuesta :

MechEngineer

Answer:

(a)€2048

(b)€4095

Step-by-step explanation:

So the amount of money we would save at nth month is

[tex]2^{n-1}[/tex] where n = 1, 2, 3, 4, ...

At the 12th month, meaning n = 12, we would save

[tex]2^{12-1}[/tex] = €2048 for that month

The total amount we would save in a year is

1 + 2 + 4 + 8 + 16 + ... + 2048

[tex]2^{n} - 1 = 2^{12} - 1 [/tex] = €4095

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