Monthly Savings Program Alice opens a savings account that pays interest per year, compounded monthly. She begins by depositing at the start of the first month and adds at the end of each month, when the interest is credited.
(a) Find a recursive formula for the amount in her account at the end of the month. (Include the interest credited for that month and her monthly deposit.)
(b) Find the first five terms of the sequence .
(c)Use the pattern you observed in (b) to find a formula for [Hint: To find the pattern most easily, it’s best not to simplify the terms too much.]
(d) How much has she saved after ?
A recursive formula for the amount at the end of the month.
An original deposit amount is and interest rate is per year compounded monthly
Saving account pays interest per year, compounded monthly. So, monthly rate of interest is,
The formula hence used will be:
The first five terms of the sequence .
A formula for .
Saved amount after .
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