Example Question - financial calculation
Here are examples of questions we've helped users solve.
Financial Calculation for University Printery Modules
The image contains a mathematical problem that requires the creation of a formula based on given charging criteria and then using that formula to calculate specific costs. Here is the problem as shown in the image: "A University printery produces student modules. The printery charges for a module depending on the size of the module, the types of cover and binding used, and the number of books in a print run. The charging formula is as follows: Charge 4 toea per page for paper and collating, and 20 toea per page for cardboard covers. Next add a charge of 5 toea per written page for printing, labour, and other page related costs; and charge K5.00 per printed page for masters that can be used for a minimum of 500 copies. Finally add 20% to the calculated cost to cover for labour costs. (a) Find a formula for a module that has P paper pages, and C cardboard covers, and is bound. Each module has 2 pages of print and the print run is 500 modules. (b) Use the formula to find the charges for a module that has 60 pages, 2 covers, and is bound. Each module has 2 pages of print and the print run is 300 modules." Let's first tackle part (a) to create a formula. Cost per paper page (for paper and collating): 4 toea Cost per cardboard cover page: 20 toea Cost per written page (for printing, labour, and other costs): 5 toea Cost per printed page for masters: K5.00 (since it can be used for a minimum of 500 copies, there is no need to multiply by the number of modules for this cost) Let's create the cost formula: Cost = (P * 4 toea) + (C * 20 toea) + (P * 5 toea) + (2 * K5.00) + 20% of the cost. To simplify: Cost = 0.09P + 0.20C + 10 + 0.20(Cost) We can't have cost on both sides of the equation, so we need to isolate it. Let's factor out the cost on the right side of the equation: Cost = 0.09P + 0.20C + 10 1.20 * Cost = 0.09P + 0.20C + 10 Cost = (0.09P + 0.20C + 10) / 1.20. This represents the total cost to produce one module. Now let's use this formula for part (b). For part (b), we have: P = 60 pages, C = 2 covers. Plugging the numbers into the formula, we get: Cost = (0.09 * 60 + 0.20 * 2 + 10) / 1.20 Cost = (5.40 + 0.40 + 10) / 1.20 Cost = 15.80 / 1.20 Cost = 13.1667. So the cost per module with 60 pages, 2 covers, and bound, with 2 pages of print for a print run of 300 modules, is approximately K13.17.
Calculating Compound Interest
To solve the compound interest problem in the image, use the formula provided: A = P(1 + r/n)^(nt) Using the information given: - Herman puts $8,000.00 into the account. - The interest earned is 5% compounded annually. - We want to know the account balance after 9 years. In terms of the variables in the formula: - P = principal amount = $8,000.00 - r = annual interest rate = 5% or 0.05 (as a decimal) - n = number of times the interest is compounded per year = 1 (since it is compounded annually) - t = the time the money is invested or borrowed for, in years = 9 Now plug these values into the formula and solve: A = 8000(1 + 0.05/1)^(1*9) A = 8000(1 + 0.05)^9 A = 8000(1.05)^9 Now calculate the right side using a calculator: A = 8000 * 1.05^9 A ≈ 8000 * 1.551328216 (rounded to 9 decimal places) A ≈ 12,410.62572 Rounding to the nearest cent, the final amount will be: A ≈ $12,410.63 So, Herman will have approximately $12,410.63 in his account after 9 years.
Calculating Investment Growth Over Time
The question states that the investment doubles every 13 years. To find out how much it will be worth after 27 years, we need to calculate how many times it will have doubled in that period. First, we divide 27 (the total number of years) by 13 (the number of years it takes to double) to find out how many doubling periods there are in 27 years: 27 years / 13 years/doubling period = 2.076923 doubling periods Since we are looking to calculate the amount to the nearest dollar, we only need whole doubling periods. So, the money will double twice in 27 years, because partial doubling periods are not complete and the question does not give us a growth rate to calculate partial periods. Starting with $220, after the first doubling period (13 years), the money will double to: $220 x 2 = $440 After the second doubling period (another 13 years, for a total of 26 years), the money will double again: $440 x 2 = $880 The investment will have doubled twice in 26 years, resulting in $880. Since 27 years includes an incomplete doubling period, and we have no rate to calculate partial growth, we stick with the amount after two full periods: $880. So, after 27 years, the person would have $880 in the account to the nearest dollar.
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