Final answer:
The value of a 5-year CD with a $1,000 initial deposit and an annual interest rate of 2% compounded annually is approximately $1,104.08. The closest provided answer choice to this calculated amount is $1,102.00, but there may be a slight discrepancy due to rounding in the options.
Step-by-step explanation:
The question asks about the future value of a 5-year Certificate of Deposit (CD) with an initial deposit of $1,000 that accrues interest at a rate of 2% per year, compounded annually. To calculate this future value, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In this case, since the interest is compounded annually:
- P = $1,000
- r = 0.02 (2% as a decimal)
- n = 1
- t = 5 years
Plugging these values into the formula, we get:
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
Thus, the value of the CD at the end of 5 years is approximately $1,104.08, which isn't an option provided. However, rounding it to the nearest dollar gives us $1,104, and if we're matching the precision of the closest given answer choices, $1,104 is closest to option b ($1,102.00). The correct answer to the question should likely be a value close to this calculated amount, but due to rounding or a mistake in the provided options, it is not exactly listed.