Final answer:
To determine how much Linda will owe after 5 years without making any payments on a $8000 loan at a 10.5% interest rate compounded monthly, the compound interest formula is used. It is found that Linda will owe $13774.89 after 5 years, rounded to the nearest cent.
Step-by-step explanation:
To calculate the amount Linda will owe after 5 years, we'll use the formula for compound interest, which is 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 Linda's case, the principal amount (P) is $8000, the annual interest rate (r) is 10.5% (or 0.105 in decimal form), the number of times the interest is compounded per year (n) is 12 (since it's compounded monthly), and the time (t) is 5 years.
Plugging these values into the formula, we get:
A = $8000(1 + 0.105/12)^(12*5)
After calculating, we find that Linda will owe $13774.89 after 5 years. This has been rounded to the nearest cent.