Final answer:
Using the compound interest formula, it's calculated that it will take just over 10 years for a $38,000 loan at 4% interest compounded annually to reach $54,000. Therefore the correct answer is d) 11 years.
Step-by-step explanation:
The question involves determining after how many years a loan of $38,000 at 4% interest compounded annually will grow to be $54,000 or more. To find this, we can use the compound interest formula:
A = P(1 + r/n)nt
Where:
- A = the amount of money accumulated after n years, including interest.
- P = the principal amount (the initial amount of money).
- r = the annual interest rate (decimal).
- n = the number of times that interest is compounded per year.
- t = the time the money is invested for, in years.
In this case:
- P = $38,000
- r = 0.04 (4% expressed as a decimal)
- n = 1 (since the interest is compounded annually)
- A = $54,000
We need to solve for t in the formula $54,000 = $38,000(1 + 0.04)t, which can be done using logarithms. After isolating t and calculating, we can find that it will take just over 10 years for the loan to reach $54,000; therefore, the answer is:
d) 11 years