At a recent family gathering you overheard your two brothers debating the merits of their vacation savings plans. Kyle, your younger brother plans to deposit $150 in his savings account at the end of this month (i. e. month 1) and then he will decrease his deposit by $10 each month over the next 18 months. Your older brother Cody would prefer to make equal monthly payments over the next 18 months rather than follow Kyle’s plan. However, he isn’t quite sure how much he would have to deposit at the end of each month (starting at the end of month one) in order to reach this goal. a. If both brothers make deposits into savings accounts that earn 1% interest per month, how much would Cody have to deposit each month in order to save the same amount as Kyle?
b. You tell your brothers that their savings plans likely won’t save sufficient money to afford their dream vacation, which will cost $1750, at the end of the 18th month. How much would Kyle and Cody have to save in order to afford this vacation? Assume that Kyle will continue to decrease his contribution in the same manner and that both brothers will continue to deposit their money into savings accounts that each 1% interest per month.