Question

You are saving money for a trip. Your plan is for each month to save 10% more money than the previous month. If you start with $100, how much will you have after 12 months? Round you answer to the nearest whole dollar.

Answer 1

Answer:  $2,138

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Explanation:

We are summing terms of a geometric sequence with

• a = 100 = first term
• r = 1.10 = common ratio representing 10% increase

To find the sum of the first n terms of a geometric sequence, use this formula

$S_n = \frac{a(1-r^n)}{1-r}$

We'll plug in the 'a' and r values mentioned, along with n = 12.

$S_n = \frac{a(1-r^n)}{1-r}\\\\S_{12} = \frac{100(1-(1.10)^{12})}{1-1.10}\\\\S_{12} \approx 2,138.428376721\\\\S_{12} \approx 2,138.43\\\\S_{12} \approx 2,138$

After 12 months, you have saved about $2,138