# Math

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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?

• Math -

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.

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