Carmen’s beauty salon has estimated monthly financing requirements for the next six months as follows: january $ 9,000 april $ 9,000 february 3,000 may 10,000 march 4,000 june 5,000 short-term financing will be utilized for the next six months. projected annual interest rates are: january 9 % april 16 % february 10 may 12 march 13 june 12 what long-term interest rate would represent a break-even point between using short-term financing and long-term financing?

9.70% annual or 0.808% per month

Explanation:

month    financing requirements       interest rate       interest charged

January            8,600                             5%                        35.83

February          2,600                             6%                          13

March              3,600                             9%                          27

April                 8,600                             12%                        86

May                  9,600                            12%                         96

June                4,600                             12%                         46

total                37,600                                                        303.83

break even annual rate = 12 months x (total interest charged / total financial requirements) = 12 x (303.83 / 37,600) = 0.096967 = 9.70% or 0.808% per month

we can check our

month    financing requirements       interest rate       interest charged

January            8,600                             9.7%                        69.49

February          2,600                             9.7%                         21.01

March              3,600                              9.7%                       29.09

April                 8,600                             9.7%                        69.49

May                  9,600                             9.7%                        77.57

June                4,600                              9.7%                        37.17

total                37,600                                                          303.82

The  total dollar interest payments for the six months is $303.33

Explanation:

The computation of the total dollar amount for the six month is shown below:

= (January financing × annual interest rate) ÷ (total number of months in a year) + (February financing × annual interest rate) ÷ (total number of months in a year) + (March financing × annual interest rate) ÷ (total number of months in a year) + (April financing × annual interest rate) ÷ (total number of months in a year) + (May financing × annual interest rate) ÷ (total number of months in a year) + (June financing × annual interest rate) ÷ (total number of months in a year)

= ($8,200 × 6.0%) ÷ 12 months + ($2,200 × 7.0%) ÷ 12 months + ($3,200 × 10.0%) ÷ 12 months + ($8,200 × 13.0%) ÷ 12 months + ($9,200 × 12.0%) ÷ 12 months + ($4,200 × 12.0%) ÷ 12 months

= $41 + $12.83 + $26.67 + $88.83 + $92 + $42

= $303.33