Question

# A local finance company quotes an interest rate of 18.1 percent on one-year loans. So, if...

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             %

 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%

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