Question

On January 1, 2006, you have $100 in a savings account that earns interest at a rate of 1% per month. On the last day of every month you deposit $75 in the account, beginning in January.

Write a recursive rule for the account balance at the beginning of the nth month.​

Answer 1

The recursive rule for account balance at the beginning of the nth month will be given by
`b_(1) = 100` and
`b_(n + 1) = b_(n) + 76` where, n = 1, 2, 3, .....

Explanation:

On January 1, 2006, I have $100 in a savings account that earns interest at a rate of 1% per month. On the last day of every month, I deposit $75 in the account, beginning in January.

So, at the end of the month of January, the added amount to the account is $75 and 1% of $100 i.e. 1$.

Then, total $(75 + 1) = $76 is being added at the end of each month.

So, the recursive rule for account balance at the beginning of the nth month will be given by
`b_(1) = 100` and
`b_(n + 1) = b_(n) + 76` where, n = 1, 2, 3, ..... (Answer)