Question

16. Ana plans to borrow $5,000 for ten years. There

is an annual interest rate of 3.99%, and three
options are available: [a] Monthly simple
interest; [b] Quarterly compound interest; or [c]
continuous compound interest. Which of option
(a, b, or c) should Ana choose?
[A] Option (c) because she earns the most in
interest ($2,451.67).
[B] Option (b) because she pays the least in
interest ($136.95).
[C] Option (a) because she earns the least in
interest ($258.45).
[D] Option (a) because she pays the least in
interest ($166.25).
[E] Option (c) because she pays the least in
interest ($495.67).

Answer 1

Ana should choose option (a) because she pays the least in interest.

To determine which option would be the most cost-effective for Ana, you need to consider the total amount of interest she would pay over the course of the loan.

Option (a) is monthly simple interest, which means that the interest is calculated on the principal balance of the loan at the end of each month, based on the annual interest rate. Option (b) is quarterly compound interest, which means that the interest is compounded and added to the principal balance of the loan at the end of each quarter. Option (c) is continuous compound interest, which means that the interest is compounded continuously, rather than at fixed intervals.

Using the formula for simple interest, the total amount of interest that Ana would pay over the course of the loan under option (a) is:

$166.25 = $5,000 * 3.99% * 10