You want to borrow R1,000 from a friend for one year, and you propose to pay her R1,120 at the end of the year.She agrees to lend you the R1,000, but she wants you to pay her R10 of interest at the end of each of the first 11 months plus R1,010 at the end of the 12th month.How much higher is the effective annual rate under your friend's proposal than under your proposal?

Question

Quizplus · Accepted Answer

Under the initial proposal, the interest rate would be (1,120-1,000)/1,000 = 12%. 
Under the friend's proposal, the total amount paid would be 11*10 + 1,010 = 1,120 which is the same as the initial proposal. However, the interest is compounding monthly so the effective annual rate would be higher than 12%. We can solve for the effective annual rate using the equation:

(1 + monthly rate)^12 - 1 = effective annual rate

Where monthly rate is (10/1,000) = 1%.

Plugging in the numbers, we get:

(1.01)^12 - 1 = 0.0084 or 0.84%

Therefore, the effective annual rate under the friend's proposal is 0.84% higher than under the initial proposal.

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