IM Alg1.5.17 Lesson: Different Compounding Intervals
Earlier, you learned about a bank account that had an initial balance of $1,000 and earned 1% monthly interest.
Each month, the interest was added to the account and no other deposits or withdrawals were made. To calculate the account balance in dollars after 3 years, Elena wrote: and Tyler wrote: . Discuss with a partner: Why do Elena's expression and Tyler's expression both represent the account balance correctly?
Kiran said, "The account balance is about ." Do you agree? Why or why not?
A credit card company lists a nominal APR (annual percentage rate) of 24% but compounds interest monthly, so it calculates 2% per month.
Write expressions for the balance on the card after 1 month, 2 months, 6 months, and 1 year.
Suppose a cardholder made $1,000 worth of purchases using
his credit card and made no payments or other purchases.
Assume the credit card company does not charge any additional
fees other than the interest. 
Write an expression for the balance on the card, in dollars, after months without payment.
How much does the cardholder owe after 1 year without payment?
What is the effective APR of this credit card?
Write an expression for the balance on the card, in dollars, after years without payment. Be prepared to explain your expression.
A bank account has an annual interest rate of 12% and an initial balance of $800. Any earned interest is added to the account, but no other deposits or withdrawals are made.
Write an expression for the account balance: After 5 years, if interest is compounded times per year.
After years, if interest is compounded times per year.
After years, with an initial deposit of dollars and an annual interest percentage rate of , compounded times per year.
Suppose you have $500 to invest and can choose between two investment options.
Which option would you choose? Build a mathematical model for each investment option and use them to support your investment decision. Remember to state your assumptions about the situation.
Is there a period of time during which the first option (3% interest rate, compounded quarterly) will always be the better option? If so, when might it be? If not, why might that be?
The function defined by models the cost of tuition, in thousands of dollars, at a local college years since 2017. What is the cost of tuition at the college in 2017?
At what annual percentage rate does the tuition grow?
Assume that before 2017 the tuition had also been growing at the same rate as after 2017. What was the tuition in 2000? Show your reasoning.
What was the tuition in 2010?
What will the tuition be when you graduate from high school?
Between 2000 and 2010 the tuition nearly doubled.
By what factor will the tuition grow between 2017 and 2027? Show your reasoning.
Choose another 10-year period and find the factor by which the tuition grows. Show your reasoning.
What can you say about how the tuition changes over any 10-year period (assuming the function continues to be an accurate model)? Explain or show how you know that this will always be the case.