Final answer:
The effective annual rate depends on the interest rate and how often it's compounded. Future values for deposits can be calculated using the compound interest formula for different interest rates and periods. A $1,000 CD with a 2% annual interest compounded annually will be worth $1,104.08 after five years.
Step-by-step explanation:
When calculating the effective annual rate (EAR) offered by a bank on a deposit, you must take into account the interest rate and the compounding frequency. To determine the amount you will have in the bank at the end of 1 year and 2 years, compound interest formulas are used.
For example, if a bank offers a 2% interest rate, compounded annually, on a 5-year CD (Certificate of Deposit), the formula to compute the future value is:
FV = P * (1 + r/n)nt
Where:
- FV is the future value of the investment/loan
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (in decimal form)
- n is the number of times that interest is compounded per year
- t is the time the money is invested for, in years
For the 5-year CD with a principal of $1,000 and an interest rate of 2% compounded annually, you would calculate the future value after 5 years like so:
FV = 1000 * (1 + 0.02/1)1*5
FV = 1000 * (1 + 0.02)5
FV = 1000 * (1.02)5
FV = 1000 * 1.10408
FV = $1,104.08
The value of the CD at the end of five years is $1,104.08.
To apply this to the scenario where you deposit $5,500, you would replace the principle (P) with $5,500 and calculate similarly based on the given interest rates and compounding frequencies for the CDs.