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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