Tough finance question- Please tell me how the equation should look on a caluclator, thank you!?

A local finance company quotes a 8 percent interest rate on one-year loans. So, if you borrow $36,000, the interest for the year will be $2,880. Because you must repay a total of $38,880 in one year, the finance company requires you to pay $38,880/12, or $3,240, per month over the next 12 months.





(a) This is not really a 8 percent loan. Instead, what is the effective monthly rate?








The correct answer is: 1.20%


Let's denote r as the effective monthly rate you need to find.


From the $36,000 loan and $3,240 monthly payment over the next 12 months, we have


PVA = $36,000 = $3,240 × {(1-[1/(1+r)]12)/r}


Solving on a financial calculator, or by trial and error, gives r = 1.2%





(b) What rate would legally have to be quoted?





The correct answer is: 14.40%


APR = 12 × 1.2% = 14.4%





(c) What is the effective annual rate?





The correct answer is: 15.39%


EAR = 1.01212 - 1 = 15.39%

Tough finance question- Please tell me how the equation should look on a caluclator, thank you!?
a) If you have a financial calculator like a Texas Instruments BA-II Plus you would have to enter the information into the N, I/Y, PV, PMT, and FV fields.





N = 12 = 12 monthly payments


PV = 36000


PMT = 3240 = montly payment


FV = 0 because at the end of the 12 months the loan is paid in full





Now you have to hit 2nd and I/Y to see the P/Y (payments/year) if you set to 1 payment a year, you will get your monthly interest rate of 1.204.....% (note the BA-II Plus gives an answer of 1.204 which is already a percent, so if it gave you 14.452 it would be 14%) or if you put in 12 payments per year you get the 14.452...% for b. When you decide which number you want hit CPT then I/Y and it will spit out either the 1.20 or the 14.45





c) Effective rate = (1 + monthly rate)^12


= (1+.01204..)^12 = 1.1544 = (1 + effective) Therefore


Effective = 0.1544 = 15.44%





I got a different answer for C because I didn't round to 1.20%, but I matched the answer you provide by using 1.20 not the computed I/Y from my calculator.

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