Final answer:
Using the compound interest formula, the future value of Janette's $20,000 loan at a 2% annual interest rate compounded annually for 5 years is $22,081.60. The closest answer choice provided is (a) $22,040.00.
Step-by-step explanation:
The student's question asks how much money Janette will owe in 5 years if she has taken out a college loan of $20,000 with an annual interest rate of 2% and the interest is compounded annually.
To find the future value of the loan, we can use the compound interest formula:
FV = P(1 + r/n)^(nt)
Where:
- FV is the future value of the loan
- P is the principal amount ($20,000)
- r is the annual interest rate (2% or 0.02)
- n is the number of times that interest is compounded per year (1, since it's compounded annually)
- t is the time in years (5 years)
Substituting the values into the formula, we get:
FV = 20000(1 + 0.02/1)^(1*5)
FV = 20000(1 + 0.02)^5
FV = 20000(1.02)^5
FV = 20000(1.10408)
FV = $22,081.60
Therefore, after 5 years without making any payments, Janette would owe $22,081.60. This means the correct answer from the provided options is (a) $22,040.00, although the last two digits should be corrected as they are slightly off from the precise calculation.