Sequences -- Quickstart -- Stretch Your Understanding

1. Suppose that you deposit $20,000 in a bank account that earns 4% interest every year. At the end of each year after the interest has been credited to your account you withdraw $1,000 for a vacation. For how many years will you be able to take a vacation in this way?

2. Suppose that you deposit $1,000 at the beginning of each year in an acccount that earns 4% interest. At the end of six years (after making the seventh deposit but before it has had a chance to earn interest) you close the account and use the money to buy a car. How much do you have to spend to buy the car? How much would you have to deposit to be able to buy a car costing $20,000? Answer the same two questions if the account earns 5% interest instead of 4% interest?

3. Bank accounts typically pay interest monthly. In this situation we use p(n) to denote the amount of money in the account at the beginning of the n-th month. Suppose that you deposit $100 per month in an account earning interest at the rate of 4% per year (or 1/3 % per month). How much money will you have in the account at the end of five years (after making the 61-st deposit but before it has had a chance to earn interest)?

4. Suppose that you borrow $25,000 at 12% interest. At the end of each year after the interest has been added to your debt you pay $4,000. In how many years will your debt be completely paid off? How much would you have to pay each year to pay the debt off in ten years? In five years?