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! 16.5% 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 16.5 percent interest, in three years you will owe: $1,000 ~ 1.1653 = $1,000 * 1.58117 = $1,581.17 Now, Judy recognizes that coming up with $1,581.17 all at once might be a strain, so she lets you make "low, low monthly payments" of $1,581.17/36 = $43.92 per month, even though this is extra bookkeeping work for her. a. What is the APR on this loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the EAR on this loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places. e.g.. 32.16.) a. APR EAR

Answer 1

a]

Monthly rate of loan is calculated using RATE function in Excel :

nper = 36 (total number of monthly payments = number of years * 12 = 3 *12 = 36)

pmt = -43.92 (Monthly payment. This is entered with a negative sign because it is a payment)

pv = 1000 (amount borrowed)

RATE is calculated to be 2.72%. This is the monthly rate. To get APR, we multiply by 12. APR is 32.66%

- : x f =RATE(36,-43.92,1000)*12 B C D E A 32.66%| 1

b]

EAR = (1 + (APR/n))ⁿ - 1

where n = number of compounding periods per year. This is 12, as the payment is monthly.

EAR = (1 + (32.66%/12))¹² - 1

EAR = 38.02%