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Suppose I earn 500 dollars every month. If I deposit my monthly income fully into the bank, the bank pays interest of 0.25 % per month on the accumulated amount from the previous month.

For example: Assuming n=months,

January, n=1, the accumulated amount would be $500

February, n=2, the accumulated amount would be $500 * 1.0025 + $500 = $1001.25

How do I find the explicit formula for the accumulated amount?

Tay Ivan
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  • Oh... I see. You're talkin' about compound interest ? – Spectre Jul 23 '20 at 08:14
  • This is a typical linear recurrence of the form$$a_{n+1}=1.0025a_n+500,\quad a_1=500$$which has the solution$$a_n=200000(1.0025^n-1)$$ – Peter Foreman Jul 23 '20 at 08:24
  • Oho..... something I can't answer. Thanks for letting me know... – Spectre Jul 23 '20 at 08:25
  • This is a very widely discussed math problem. For example, here's essentially the same problem, with the solution :https://math.stackexchange.com/questions/3164490/market-price-pt-at-any-time/3164532#3164532 – Matti P. Jul 23 '20 at 08:27

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