Question

compound interest with non-annual periods after examining the various personal loan rates available to you do you find that you can borrow funds from the finance company at a APR of 7% compounded annually or from a bank at an APR 8% compounded monthly which alternative is more attractive

Answer 1

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Correct Answer: One must prefer a finance company with APR 7 % compounded annually.

Reasoning :

Since the other option is compounded monthly we need to find the effective annual interest rate to make a comparison between the two

Now we have Two Options

Option 1) APR 7 % Compounded annually

Option 2) APR. 8 % Compounded monthly.

Converting Option 2 into

Now finding the Effective Annual interest rate,

Effective Annual interest rate = ( 1 + (i/n) )n - 1

Where i is the nominal interest rate

and n is the number of periods

Substituting the values from the question

Effective Annual interest rate for option 2 =  (1 + (0.08 / 12))12 -1

Effective Annual interest rate for option 2 = ( 1 + 0.0067)12 -1

Effective Annual interest rate for option 2 = 1.0830 -1

Effective Annual interest rate for option 2 = 0.0830 or 8.30 %

Therefore, Option 1 with APR 7 % compounded annually is a better option than Option 2 with Effective annual interest rate of 8.30 %