This activity will you meet these educational goals:
you will create and use an exponential expression to model financial situations with an interest rate and manipulate this expression to be used over different compounding periods of time.

emma doesn’t have experience using credit cards. in fact, she just got her first one. she is also about to start her first year of college. she uses her new credit card to purchase textbooks for her classes. the total comes to $300. these are the terms of her credit card:

it has a 15% yearly interest rate.
the interest is compounded monthly.
the card has $0 minimum payments for the first four years it is active.
the expression that models this situation is p(1+r/n)^nt ,where (1+r/n)represents the growth factor of the interest rate.

part a
identify the values of p, r, and n in the expression p(1+r/n)^nt based on the verbal description of the emma’s situation. then, substitute those values into the formula to form an expression in terms of time.

part b
emma doesn’t have $300 now, but she plans to get a job when she gets to college. she wants to find out how much it will cost her if she doesn’t pay off her credit card until after college. find how much she’ll owe in four years.
part c
emma notices that since her credit card compounds monthly, she is charged more than 15% of her initial loan amount in interest per year. she wants to know how much she would pay if the card were compounded yearly at a rate of 15%. find the numeric expression to evaluate a yearly compounding interest rate.
part d
using the formula you just found, determine how much emma would owe after four years if the interest were compounded yearly instead of monthly. round your answer to the nearest penny.