Question

A local finance company quotes an interest rate of 18.3 percent on one-year loans. So, if you borrow $40,000, the interest for the year will be $7,320. Because you must repay a total of $47,320 in one year, the finance company requires you to pay $47,320/12, or $3,943.33 per month over the next 12 months. What rate would legally have to be quoted? (APR) What is the effective annual rate? (EAR)

Answer 1

What rate would legally have to be quoted? (APR) = 32.22 %

What is the effective annual rate? (EAR) = 37.43 %

Explanation

We have 40000 as present value. And the present value of future payments must be equal to this 40,000.

Thus ......... 3943.33 * [ 1 - (1+r)^-n ] / r = 40000.

Here n = nper = number of periods = 12

r = monthly APR ........... to be computed.

We use RATE function in excel to find he accurate value of .......... " r "

= RATE(nper, pmt, pv,[fv],[type])

Here .........nper = 12 ...........pmt = - 3943.33 ......... pv = 40000 and put ....... pv = 0 and type = 0

=RATE(12,-3943.33,40000,0,0,2) ........... this function will give .......... r = 2.685%

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

= 2.685 * 12 months = 32.22 %

What is the effective annual rate? (EAR)

EAR = ( 1 + APR/m )^m - 1

= ( 1 + 2.685% )¹² - 1

= (1.02685)¹² - 1 = 0.3743 ........... or ........ 37.43 %