Question

Nominal Rate of Return

Anne Lockwood, manager of Oaks Mall Jewelry, wants to sell on credit, giving customers 3 months to pay. However, Anne will have to borrow from her bank to carry the accounts receivable. The bank will charge a nominal rate of 6% and will compound monthly. Anne wants to quote a nominal rate to her customers (all of whom are expected to pay on time) that will exactly offset her financing costs. What nominal annual rate should she quote to her credit customers? Do not round intermediate calculations. Round your answer to two decimal places.

  %

Answer 1

We have to quote that APR for which Effective annual rate of borrowing from bank and lending to customers is same.

Bank charges Nominal rate (r) = 6%

number of compounding in year for monthly compounding (m) is 12

Effective annual rate formula = ((1+(r/m))^m)-1

=((1+(6%/12))^12)-1

=0.06167781186 or 6.167781186%

customers Credit time = 3 months

number of 3 month compounding in a year (m) =12/3 =4

Effective annual rate of lending at APR r must be same as borrowing

0.06167781186 = ((1+(r/4))^4)-1

0.06167781186+1 = (1+(r/4))^4

(1.061677812)^(1/4) = (1+(r/4))

1.015075125-1 = r/4

0.015075125*4 = r

r =0.0603005 or 6.03%

So nominal annual rate quoted to customers should be 6.03%