Final answer:
The effective annual interest rate (EAR) for a bank CD paying 8.02% compounded annually is 8.02%, because it is compounded once yearly. For a 5-year CD with $1,000 at 2% interest compounded annually, the value after five years would be $1,104.08.
Therefore, the value of the CD at the end of the five years is $1,104.08
Step-by-step explanation:
To calculate the effective annual interest rate (EAR) for a bank CD paying 8.02% compounded annually, you would use the formula for EAR:
EAR = (1 + nominal rate/number of compounding periods)^number of compounding periods - 1
In this case, the nominal rate is 8.02% (or 0.0802 as a decimal), and since the interest is compounded annually, the number of compounding periods is 1. Plugging these values into the formula gives:
EAR = (1 + 0.0802/1)^1 - 1
EAR = (1 + 0.0802) - 1
EAR = 1.0802 - 1
EAR = 0.0802
Converted back into a percentage, the EAR is 8.02%, which is the same as the nominal rate because the interest is compounded annually only once per year.
When it comes to the example question provided, if you open a 5-year CD for $1,000 that pays 2% interest compounded annually, the value at the end of the five years is calculated using the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- P is the principal amount ($1,000)
- r is the annual interest rate (2% or 0.02)
- n is the number of times that interest is compounded per unit t (annually, so n=1)
- t is the time the money is invested for (5 years)
A = $1,000(1 + 0.02/1)^(1*5)
A = $1,000(1 + 0.02)^5
A = $1,000(1.02)^5
A = $1,000(1.10408)
A = $1,104.08
Therefore, the value of the CD at the end of the five years is $1,104.08.