Question 1196613
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Let A be the amount she withdrew each day: {{{A = 125}}}<br>
Let r be the daily growth factor based on the (annual) interest rate of 28%: {{{r = 1+.28/365}}}<br>
By the time she returns home...<br>
the balance from her withdrawal on day 1 was {{{Ar^20}}}
the balance from her withdrawal on day 2 was {{{Ar^19}}}
...
the balance from her withdrawal on day 19 was {{{Ar^2}}}
the balance from her withdrawal on day 20 was {{{Ar^1}}}
the balance from her withdrawal on day 21 was {{{Ar^0}}}<br>
Those daily balances form a geometric sequence; the sum of the balances is<br>
{{{A((1+r)^21-1)/(1+r))}}}<br>
Use a calculator with the values of A and r to find the balance is $2645.24.<br>
This answer can also be confirmed using a spreadsheet.  Start with $125, multiply by the daily growth factor, add another $125, multiply again by the daily growth factor; and repeat for 21 days (but don't apply the growth factor on the last day).<br>
The total amount of her withdrawals was 21($125) = $2625, so the amount of interest she paid was $20.24.<br>
ANSWERS: balance $2645.24; interest $20.24<br>