question text WITH missing information:
After examining the various personal loan rates available to you, you find that you can borrow funds from a finance company at an APR of 12 percent compounded monthly or from a bank at an APR of 13 percent compounded annually. Which alternative is more attractive?
If you borrow $100 from a finance company at an APR of 9% percent compounded for year, how much do you need to payoff the loan?
Answer:
The finance company option is better as we are taking the loan we want the lower rate possible.
We need $109 to payoff the loan of $100 at 9% annualy after a whole year.
Explanation:
We solve for the effective rate of 12% compounded monthly
[tex](1+\frac{0.12}{12} )^{12}[/tex] = 1.12682503 = 0.126825 = 12.6825%
As this rate is lower than 13% this option is better
If we take 100 dollars after a year we have to pay:
$100 x (1 + r) = 100 x (1 + 0.09) = 100 x 1.09 = $109
