Question

As a jewelry store manager, you want to offer credit, with interest on outstanding balances paid monthly. To carry receivables, you must borrow funds from your bank at a nominal 7%, monthly compounding. To offset your overhead, you want to charge your customers an EAR (or EFF%) that is 3% more than the bank is charging you. What APR rate should you charge your customers? Round your answer to two decimal places.

Answer 1

Computation of APR that should be charged to customers:
To find APR let us use the EAR formula:
EAR = ( 1 + ( APR / 12 )¹² ) - 1
Here, as per the given information:
EAR = (1+ (monthly nominal rate))^12months)-1
= ( 1 + ( 7% / 12 ))¹² ) - 1
= 0.07229 + 0.03 = 0.10229
Thus, substituting EAR in the EAR formula:
EAR = ( 1 + ( APR / 12 )¹² ) - 1
0.10229 = (1+(APR/12)¹²-1
1.10229 = ( 1 + ( APR / 12 )¹² )
( 1.10229 )^{( 1/12 )} = 1 + ( APR / 12 )
1.008149 = 1 + ( APR / 12 )
0.008149 = APR / 12
APR =0.008149*12 = 0.097786
Therefore, APR= 9.78%