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.
a.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________ %

b.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

Answer:

The legal rate to quote is 31.88%   per year

The effective annual rate is 36.98%

Explanation:

In calculating the legal rate, I used the rate function in excel,whose formula is below:

rate(nper,-pmt,pv)

The nper is the period of loan calculate as 1 year multiplied by 12 months

pmt is the periodic monthly loan repayment of $3838.25

pv is the today's value of the loan at $39000

Find detailed computation in the attached spreadsheet.

Download xlsx