A local finance company quotes an interest rate of 16.4 percent on one-year loan

Question

A local finance company quotes an interest rate of 16.4 percent on one-year loans. So, if you borrow $32,000, the interest for the year will be $5,248. Because you must repay a total of $37,248 in one year, the finance company requires you to pay $37,248/12, or $3,104.00 per month over the next 12 months.

3. What is the effective annual rate? (Round your answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

A local finance company quotes an interest rate of 16.4 percent on one-year loans. So, if you borrow $32,000, the interest for the year will be $5,248. Because you must repay a total of $37,248 in one year, the finance company requires you to pay $37,248/12, or $3,104.00 per month over the next 12 months.

Explanation / Answer

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 = 33000
PMT = 3104 = 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%

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