Math Homework Assignment: Financial Calculations and Analysis

This document provides a comprehensive solution to a math homework assignment. The assignment covers a range of financial concepts including calculating the total cost of a car with simple interest, determining the final retail price of an item with markup and tax, solving compound interest problems, analyzing commission-based salary structures, calculating depreciation using different methods, and performing break-even analysis. The solutions include detailed calculations and explanations for each problem, providing a clear understanding of the concepts and methodologies used. Furthermore, the assignment covers the calculation of profit and loss based on sales and cost analysis. The solution provides a step-by-step approach to solve each question, ensuring a thorough understanding of the topics covered.

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Question 1
Total price of car = $ 12,995
Initial down-payment = $ 3,500
Total amount borrowed = 12995 – 3500 = $9.495
Total amount paid = Principal + Simple Interest
Simple Interest = P*R*T
Where P = Sum borrowed or $ 9,495
R = Rate of interest or 12%
T = Time period or 6 years
Hence, simple interest on the borrowed amount = 9495*0.12*6 = $ 6.836.4
Therefore total cost of the car including interest = 12995 + 6836.4 = $ 19,831.40
Question 2
(a) Cost price = $ 137
Mark up = 33.33% or (100/3)%
Hence, marked up price = 137 *(1+(100/300)) = $182.67
On the above price, a retail tax of 20% is applied
Final retail price of the book = 182.67*(1+(20/100)) = $ 219.2
(b) Now the value of the retail tax is $ 14
Price before retail tax = $182.67
Hence, final retail price of the book = 182.67 + 14 = $ 196.67
Question 3
(a) The formula for simple interest is as follows.
Simple interest = P*R*T
Total simple interest desired = $ 5,300

Time period T = 1 year for both principal amounts
Let the principal amount in second account be P
Then, 5300 = 22000*0.16*1 + P*0.125*1
Solving the above, we get P = $ 14,240
(b) Let the requisite amount invested be denotes as P
Interest rate (R) = 8% p.a. or 2% per quarter
Final amount (A) = $ 10,000
Time period (T) = 4 years or 16 quarters
The relevant formula to be used is as follows.
A = P (1+R)T
Substituting the requisite input values, we get
10000 = P(1.02)16
Solving the above, we get P= $7,284.46
Question 4
Current Salary = $ 30,000 p.a.
Under the choice offered $ 10,000 is the fixed salary and therefore if the same amount of
salary would have to be earned in this proposed plan, then commission to the tune of $
20,000 ought to be derived.
Commission amount of first $ 100,000 of sales = (3.75/100)*100000 = $ 3,750
Commission amount on the next $ 200,000 of sales = (6.5/100)*200000 = $ 13,000
Total commission income derived from $ 300,000 sales per annum = 3750 + 13000 = $
16,750
Incremental commission required to match the current salary = 20000-16750 = $ 3,250
A commission of 9% would be paid on sales above $ 300,000 per annum. Let the requisite
sales amount above $ 300,000 be $ X
Then (9/100)*X = 3250
Solving the above, X = $36,111

Hence, it can be concluded that in order to have the same salary under the proposed plan,
annual sales of $ 336,111 need to be generated.
Question 5
(a) Initial cost= $35,000
Since 21% is depreciated each year, hence 79% of value remains.
Value of the car at the end of year 4 = 35000*0.794 = $13,633
(b) Initial cost = $ 110,000
Since 12% is depreciated each year, hence 88% of value remains.
Value of the furniture at the end of year 7 = 110000*0.887 = $44,954
(c) Total depreciation over the useful life of 100,000 hours = Initial cost – Scarp value =
137000-30000 = $107,000
Depreciation per hour = 107,000/100000 = $1.07
Total depreciation for 19000 hours = 1.07*19000 = $20,330
Question 6
(a) Unit selling price = $ 6.50
Unit variable cost = $ 1.80
Unit contribution margin = Unit selling price – Unit variable cost = 6.5 – 1.8 = $ 4.7
Units required for break-even = Fixed cost/Unit contribution margin = 800/4.7 = 170.2 or 171
toys
(b) Break even number of toys is 171
Cost of making break even number of toys = Fixed cost + variable = 800 + 171*1.8 = $
1,107.8
(c) Cost required to make 180 toys = 800 + 180*1.8 = $1,124
(d) Sales proceeds obtained by selling 180 toys = 180*6.5 = $ 1,170
(e) Profits earned by selling 180 toys = Sales proceeds – Cost = 1170 -1124 = $ 46
Question 7
Contribution margin

Sales price per photo album = $ 35.50
Purchase price per photo album = $ 18.50
Unit contribution margin = 35.50 -18.50 = $ 17
Annual fixed cost
The annual fixed cost would comprise of the following elements.
Rent = $20,000, Telephone = $ 4,000, Staff wages = $ 50,000, Superannuation = $ 4,750,
Printing = $ 4,800
Hence, total fixed cost = 20000 + 4000 + 50000 + 4750 + 4800 = $83,550
Breakeven Point
Breakeven Volume = Fixed cost/Contribution margin = 83550/17 = 4915 photo albums
Proof of statement
Sales revenue from 4915 photo album sale = 4915*35.5 =$ 174,482
Variable cost for 4915 photo album = 4915*18.5 = $ 90,928
Annual fixed cost = $ 83550
Annual fixed cost + variable cost approximate equals the sales revenue which provides the
proof for break even being sale of 4915 units annually.