Business Math
Practice Exam 2 Solutions
Sections 7.1 – 7.4, 8.1 – 8.4
NAME:
Include work for partial credit. Proofread your written answers. Please circle your final
answer, especially if there is a lot of work. The numbers in parentheses by each question
number is the point value of that question. On the last page, you will find a chart listing the
number of each of the days of the year.
Write your numbers neatly using commas and dollar signs where appropriate in your final
answers. Round dollars and cents to two decimal places. Round percents to the nearest
tenth of a percent, unless specified otherwise.
1. (3) In your own words, what is markup?
Markup is the amount a store adds to the cost of an item to determine the selling price. Markup
covers their operating expenses and desired profit.
2. (6) A restaurant buys a steak for $15 and sells it for $25. Find the markup in the following
three forms.
a.) Find the dollar value of the markup.
$25 – $15 = $10
b.) Find the markup percent on cost.
10
= .67 or 67 %
15
c.) Find the markup percent on selling price.
10
= .4 or 40%
25
3. (4) A local bookstore buys the latest John Grisham novel for $4.55. They want to add a
markup of 18% based on cost. Find the selling price of this novel.
Find 18% of the cost (to find the markup). --- .18 ∗ 4.55 = .82 or $ .82
Add that to the cost (to find the selling price). --- .82 + 4.55 = 5.37 or $5.37
4. (9) Bob’s Barbershop sells various hair care products. The table below shows the cost and
selling price for several items. Answer the questions that follow.
Item
Shampoo (16 oz)
Conditioner (16 oz)
Styling Gel (5 oz)
Hairspray (10 oz)
Cost
$2.50
$3.25
$3.25
$3.00
Selling price
$3.75
$4.25
$4.25
$4.00
Markup
$1.25
$1
$1
$1
a.) Complete the table to find the markup for each item.
b.) Last month, Bob’s Barbershop sold 6 bottles of shampoo, 5 bottles of conditioner, 3 bottles
of styling gel, and 3 bottles of hairspray. Calculate the markup percent based on selling price for
that month.
Total markup --- 6 ∗1.25 + 5 ∗1 + 3 ∗1 + 3 ∗1 = 18.50 or $18.50
Total selling price --- 6 ∗ 3.75 + 5 ∗ 4.25 + 3 ∗ 4.25 + 3 ∗ 4 = 68.50 or $68.50
Percent markup on selling price equals markup divided by selling price or
M 18.5
=
= .270 or 27.0 %
S 68.5
c.) Consider the sales of last month as described in part b. Calculate the percent markup on cost
% markup on selling price
. Show your work.
using the formula % markup on cost =
100% − % markup on selling price
% markup on selling price
100% − % markup on selling price
.27
=
1.00 − .27
.27
=
.73
= .3699
% markup on cost =
Now, .3699 rounds to .370 (since the
fourth digit (being 5 or greater)
rounds the third digit to 0, which in
turn rounds the second digit to 7. So
markup on cost is 37.0%.
5. (3) Olympic Sports has an end-of-season sale during which it sells a ProForm Upright Bike for
$265. If the cost was $198 and the operating expenses were 25% of cost, find the amount of
profit or loss. Label it as profit or loss.
Their cost plus operating expenses are 198 + .25 ∗198 = 247.50 or $247.50. Since they sold it for
more than that, they made a profit. We subtract to find their profit of $17.50.
6. (4) A furniture store buys a sofa (bright orange with big blue flowers) for $450. Their
operating expenses were 20% of cost. They originally put a price tag of $700 on the sofa.
Strangely, they had to mark down the sofa to $500 to get it to sell. Answer the following
questions.
a.) Did the store incur an operating loss or an absolute loss?
Find the Break-even point which is cost plus operating expenses. This would be
450 + .2 ∗ 450 = 540 or $540. They would incur an operating loss if this was more than the
reduced selling price. They would incur an absolute loss if the cost alone was more than the
reduced selling price. Since the cost was $450 and the reduced selling price was $500, they did
not incur an absolute loss. However, they did incur an operating loss since the break-even point
of $540 was more than the reduced selling price of $500.
b.) Calculate the loss.
Operating loss = Break-even point – Reduced selling price
Operating loss = 540 - 500 = 40 or $40.
7. (3) Find the average inventory for the company whose quarterly inventory amounts are listed
below.
Date
January 1
April 1
July 1
October 1
Inventory Amount at Retail
$54,230
$65,450
$62,300
$75,000
The average inventory is found by adding the inventories taken and then dividing by the total
number of times the inventory was taken. I do this below.
54, 230 + 65, 450 + 62,300 + 75, 000
= 64, 245 or $62,245
4
8. (3) Last month Margaret’s Margaritas, a popular neighborhood bar, had an average retail
inventory of $15,000 and retail sales of $26,500. Find the stock turnover at retail. Round to the
nearest hundredth (two decimal places).
Turnover at retail is found by dividing retail sales by the average inventory at retail. I do this
below.
26,500
= 1.77
15, 000
This is interpreted as the number of times that the value of the inventory has sold during the
month in question.
9. (3) Joe borrows $50,000 at the simple interest rate of 5% for 9 months. How much interest
will he be charged?
Use the simple interest formula. Before using any formula, be sure you know what the variables
represent. Make sure you write the rate in decimal form and convert 9 months to years by
dividing by 12.
I = PRT
( 12 )
= 50, 000 ∗ .05 ∗ 9
= 1875
So he will be charged $1875 in interest.
10. (2) In general, what is the relationship among interest, principal, and maturity value?
Maturity value is how much is in the account at the end of the investment period. Principal is the
initial deposit or investment. Interest is the money you earn on that principal. So maturity value
is equal to principal plus interest.
11. (2) Refer to the chart on the last page for this question. Find the number of days from April
12 to October 13.
April 12 is day 102. October 13 is day 286. Subtract 102 from 286 to get 184. So there are 184
days between April 12 and October 13.
12. (4) Refer to the chart on the last page for this question. A local aquarium borrowed $55,000
to renovate their front entrance. They borrowed the money at 7% simple interest on May 17.
They plan on paying their loan off on December 31. Answer the following questions.
a.) Calculate the interest they owe using ordinary (or banker’s) interest.
May 17 is day 137 and December 31 is day 365. So the number of days they borrowed the money
is 228. Use the simple interest formula. Write the rate as a decimal and divide the number of
days by 360 to convert to years. Notice we are using 360 here because we are to use banker’s
interest.
I = PRT
(
= 55, 000 ∗ .07 ∗ 228
360
)
They will pay $2438.33 in interest.
= 2438.33
b.) How much would they need to pay back on December 31?
They will need to pay back the principal (how much they borrowed) plus the interest. So they will
pay back $2438.33 + $55,000 or $57,438.33 total.
13. (3) Bob has just repaid a loan. He was loaned $10,000 and had four months to repay the loan.
He was charged $654 in interest. Find the interest rate.
Use the simple interest formula with R isolated. You have to remember to use 4/12 for T.
R=
=
I
PT
654
( 12)
10, 000 ∗ 4
= .1962
Be careful with how you put this into the calculator. If you put it all in
at once, you need parentheses around the bottom. Input
654 / (10000 ∗ 4 / 12) and it will work. If you do it piece by piece, do
not round your intermediate answers or you will be slightly off at the
end.
Round the final answer to .196 and interpret as 19.6%.
14. (4) A simple discount note has a face value of $1,000 and a discount rate of 13%. The note
was made on May 5 and will mature in 180 days. Answer the following questions.
a.) What is the maturity date of the note?
May 5 is day 125 according to the table. Add 180 to 125 to get 305. Then look 305 in the table to
find that is November 1. The maturity date is November 1.
14 b.) Calculate the proceeds (or loan amount). [Use banker’s interest.]
The proceeds equals face value minus bank discount. First, find the bank discount. I do it below.
B = MDT
(
= 1000 ∗ .13 ∗ 180
360
)
= 65
So the bank discount is $65. Subtract that from the face value of $1,000 to find the proceeds of
$935.
15. (8) My brother’s law firm signed a 1 year simple discount note with a face value of $50,000
and a rate of 8% on June 4. The lender sold the note on December 12 at a 7% discount rate.
Answer the following questions.
a.) Find the proceeds of the original note to the law firm.
B = MDT
P=M −B
= 50, 000 ∗ .08 ∗1
= 4000
= 50, 000 − 4, 000
= 46, 000
So the proceeds (how much
the law firm receives) is
$46,000.
b.) Find the discount period.
The discount period is the number of days from the sale of the note to the maturity date of the
note. The maturity date of the note is June 4, one year after they signed the note. The time of the
sale is December 12 the year before. So the number of days in the discount period would be the
number of days from December 12 to the end of the year (found to be 365 – 346 or 19) plus the
number of days from the beginning of the year to June 4 (found to be 155). Add 19 plus 155 to
get a discount period of 174 days. Notice this uses the table heavily.
c.) Find the bank discount for the sale of the note on December 12.
B = MDT
(
= 50, 000 ∗ .07 ∗ 174
360
)
The bank discount is $1,691.67.
= 1691.67
d.) Find the proceeds at the sale of the note on December 12.
P=M −B
= 50, 000 − 1, 691.67
= 48,308.33
The proceeds of the sale is $48,308.33.
The Number of Each of the Days of the Year Day of month Jan. Feb.
1 1 32 2 2 33 3 3 34 4 4 35 5 5 36 6 6 37 7 7 38 8 8 39 9 9 40 10 10 41 11 11 42 12 12 43 13 13 44 14 14 45 15 15 46 16 16 47 17 17 48 18 18 49 19 19 50 20 20 51 21 21 52 22 22 53 23 23 54 24 24 55 25 25 56 26 26 57 27 27 58 28 28 59 29 29 30 30 31 31 Mar. 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 Apr. May
91 121
92 122
93 123
94 124
95 125
96 126
97 127
98 128
99 129
100 130
101 131
102 132
103 133
104 134
105 135
106 136
107 137
108 138
109 139
110 140
111 141
112 142
113 143
114 144
115 145
116 146
117 147
118 148
119 149
120 150
151
Jun.
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
Jul.
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
Add 1 to each day after February 29 for leap years.
Aug.
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
Sep.
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
Oct.
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
Nov. Dec. Day of month
305 335 1
306 336 2
307 337 3
308 338 4
309 339 5
310 340 6
311 341 7
312 342 8
313 343 9
314 344 10
315 345 11
316 346 12
317 347 13
318 348 14
319 349 15
320 350 16
321 351 17
322 352 18
323 353 19
324 354 20
325 355 21
326 356 22
327 357 23
328 358 24
329 359 25
330 360 26
331 361 27
332 362 28
333 363 29
334 364 30
365 31