Question

Rita has deposited $1000 in a bank account. At the end of each year, the bank posts interest to her account in the amount of 5% of the balance, but then takes out a $10 annual fee.

Recursions and Special Sequences

Answer 1

Rita will have $1040 in her bank account by the end of the year.

Explanation:

To know how much money will Rita have in her account by the end of the year, we have to perform the following calculation:

$1000 (initial amount) + $1000x5/100 (annual interest) - $10 (annual fee) = X (total money)

1000 + 1000x5/100 - 10 = X

1000 + 50 - 10 = X

1040 = X

Rita will have $1040 in her bank account by the end of the year.

Answer 2

b[0] = 1000
b[n+1] = 1.05*b[n] -10

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The fee has the effect of negating the interest earned on the first $200. Effectively, Rita's account balance in explicit form is 200 +(b0 -200)*1.05^n.