Question

# A local finance company quotes an interest rate of 18.3 percent on one-year loans. So, if...

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)

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 %