1. A couple wants to open a savings account with $1,500 and keep the money in it for two years. Their bank offers two accounts, A and B. They calculate that the balance of Account A after two years will be about $1,548.74. Account B earns 1.9% annual interest compounded semiannually. There is also a $7 annual fee that is reduced to $4 if the balance is $2,500 or more. The fee is deducted at the end of the year.
a. What will be the balance of Account B after two years? Round to the nearest cent as needed.
b. Which account should they choose?
2. Haley wants to open a savings account with $2,460 and keep the money in it for two years. Her bank offers the following accounts. The fee for Account B is deducted at the end of the year.
Account A: 1.5% annual interest, compounded monthly No annual fee
Account B: 1.2% annual interest, compounded weekly $4 annual fee
∗for accounts with a balance of $2,500 or more; otherwise $7
a. What will be the balance of each account after two years? Round to the nearest cent as needed.
b. Which account should she choose?
3. Julia wants to open a savings account with $2,462 and keep the money in it for three years. Her bank offers the following accounts. The fees are deducted at the end of the year.
Account A: 1.4% annual simple interest $6 annual fee
Account B: 1.5% annual interest, compounded weekly $5 annual fee
∗for accounts with a balance of $2,500 or more; otherwise $6
a. What will be the balance of each account after three years? Round to the nearest cent as needed.
b. Which account should she choose?
c. Should Julia consider anything other than the final balance when choosing an account? Explain.
4. Aaron wants to open a savings account with $2,444 and keep the money in it for three years. His bank offers two accounts, A and B. He calculates that the balance of Account A after three years will be about $2,545.80. Information about Account B is shown below. The fee is deducted at the end of the year.
Account B: 1.8% annual interest, compounded semiannually $5 annual fee
∗ for accounts with a balance of $2,500 or more; otherwise $6
Which account will have the greater balance at the end of three years? How much greater will it be? Round to the nearest cent as needed.
5. Think About the Process Eric wants to open a savings account with $2,450 and keep the money in the account for three years. His bank offers the following accounts. The fees are deducted at the end of the year.
Account A: 1.5% annual interest, compounded quarterly $6 annual fee
Account B: 1.6% annual interest, compounded semiannually $5 annual fee
∗ for accounts with a balance of $2,500 or more; otherwise $8
He wants to use the compound interest formula, B=p(1 + r)^{ n }, to find the balance of each account at the end of each year.
a. What should he substitute for r in Account A?
b. What should he substitute for r in Account B?