Math
posted by Queen on .
Acton choose from two loans offersS: 12,000 at 8% simple interest for 9 months: or a 12,000 9 month discounted loan at 7% discount. Based on the actual interest paid and the true rate on the discounted loan, which of the two loan offers will Acton choose?

For the simple loan what is the interest rate paid for 9 months?
Interest paid = .08(9/12)(12,000) = 720
r = what you paid/what you got = 720/12,000 = .06
what is the real interest rate on the discounted loan?
Well, how much is the nominal interest paid?
I = .07 * (9/12)(12,000) = 630 looks cool but
what you got = 12,000  630 = 11,370
so
r = 630/11370 = .055
so you are half a percent better off with the discounted loan, although you walk out of the bank with less than the 12,000 you needed.