Question

A local finance company quotes an interest rate of 18.1 percent on one-year loans. So, if you borrow $39,000, the interest for the year will be $7,059. Because you must repay a total of $46,059 in one year, the finance company requires you to pay $46,059/12, or $3,838.25 per month over the next 12 months.

What rate would legally have to be quoted? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

APR             %

What is the effective annual rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

EAR             %

Answer 1

1)	The rate to be quoted is the APR.
	The monthly rate would be that rate which equates
	the PV of the monthly payments of $3838.95 with
	the loan amount of $39000.
	So, 39000 = 3838.95*PVIFA(r,12), where r is the
	monthly interest rate.
	PVIFA(r,12) = 39000/3838.95 = 10.1590
	From the PV interest tables
	interest factor for 2% for 12 periods = 10.5753
	and for 3% it is 9.9540.
	Hence, interest rate for factor of 10.1590 = 2%+1%*(10.5753-10.1590)/(10.5753-9.9540) =	2.67%
	APR = 12*2.67% =	32.04%
2)	EAR = 1.0267^12-1 =	37.19%