This problem illustrates a deceptive way of quoting interest rates called add-on

Question

This problem illustrates a deceptive way of quoting interest rates called add-on interest. Imagine that you see an advertisement for Crazy Judy’s Stereo City that reads something like this: “$1,000 Instant Credit! 18% Simple Interest! Three Years to Pay! Low, Low Monthly Payments!” You’re not exactly sure what all this means and somebody has spilled ink over the APR on the loan contract, so you ask the manager for clarification.

Judy explains that if you borrow $1,000 for three years at 18 percent interest, in three years you will owe:

Judy recognizes that coming up with $1,643.03 all at once might be a strain, so she lets you make “low, low monthly payments” of $1,643.03 / 36 = $45.64 per month, even though this is extra bookkeeping work for her.

What is the APR on this loan? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What is the EAR? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

This problem illustrates a deceptive way of quoting interest rates called add-on interest. Imagine that you see an advertisement for Crazy Judy’s Stereo City that reads something like this: “$1,000 Instant Credit! 18% Simple Interest! Three Years to Pay! Low, Low Monthly Payments!” You’re not exactly sure what all this means and somebody has spilled ink over the APR on the loan contract, so you ask the manager for clarification.

Explanation / Answer

EMI = Amount to be financed*Monthly interest rate*(1+Monthly interest rate)No. of months / [(1+Monthly interest rate)No. of months - 1]

=> $45.64 = $1,000*Monthly interest rate*(1+Monthly interest rate)36 / [(1+Monthly interest rate)36 - 1]

By trial and error method,

Monthly interest rate = 2.976%

Annual percentage rate = Monthly interest rate*12

= 2.976%*12

= 35.710%

Effective annual rate = [(1+Monthly interest rate)12 - 1]*100%

= [(1+2,976%)12 - 1]*100%

= 42.178%

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