Basic Math Questions and Answers

9 Implied interest rate and period Consider the case of the following annuities and the need to compute either their expected rate of return or duration Matthew needed money for some unexpected expenses so he borrowed 3 900 55 from a friend and agreed to repay the loan in four equal installments of 1 100 at the end of each year The agreement is offering an implied interest rate of Matthew s friend Gregory has hired a financial planner for advice on retirement Considering Gregory s current expenses and expected future lifest changes the financial planner has stated that once Gregory crosses a threshold of 4 136 860 in savings he will have enough money for retirement Gregory has nothing saved for his retirement yet so he plans to start depositing 40 000 in a retirement fund at a fixed rate of 5 00 at the end of each year It will take for Gregory to reach his retirement goal

7 Future value of annuities There are two categories of cash flows single cash flows referred to as lump sums and annuities Based on your understanding of annuities answer the following questions Which of the following statements about annuities are true Check all that apply A perpetuity is a series of equal payments made at fixed intervals that continue infinitely and can be thought of as an infinite annuity When equal payments are made at the end of each period for a certain time period they are treated as ordinary annuities An ordinary annuity of equal time earns less interest than an annuity due When equal payments are made at the end of each period for a certain time period they are treated as an annuity due Which of the following is an example of an annuity An investment in a certificate of deposit CD A lump sum ayment made to a life insurance company that promises to make a series of equal payments later for some Ashley has a large and growing collection of animated movies She wants to replace her old television with a new LCD model so she has started saving for it At the end of each year she deposits 1 060 in her bank account which pays her 7 interest annually Ashley wants to keep saving for two years and then buy the newest LCD model that is available Ashley s savings are an example of an annuity How much money will Ashley have to buy a new LCD TV at the end of two years 1 865 07 of time O 2 194 20 O 2 347 79 O 1 916 50 by the end of two

14 Loan amortization and capital recovery After Shipra got a job the first thing she bought was a new car She took out an amortized loan for 45 000 with no 0 down payment She agreed to pay off the loan by making annual payments for the next four years at the end of each year Her bank is charging her an interest rate of 10 per year Yesterday she called to ask that you help her compute the annual payments necessary to repay her loan Calculate the annual payment and complete the following loan amortization table Year Beginning Amount 1 2 3 4 45 000 00 Payment Interest Paid 4444 Principal Paid Ending Balance 0 02

Open spreadsheet a Complete an amortization schedule for a 45 000 loan to be repaid in equal installments at the end of each of the next three years The interest rate is 10 compounded annually Round all answers to the nearest cent Year 1 2 3 Year 1 Year 2 Year 3 Beginning Balance Interest Payment Principal b What percentage of the payment represents interest and what percentage represents principal for each of the three years Round all answers to two decimal places Interest Repayment of Principal Ending Balance c Why do these percentages change over time I These percentages change over time because even though the total payment is constant the amount of interest paid each year is declining as the remaining or outstanding balance declines II These percentages change over time because even though the total payment is constant the amount of interest paid each year is increasing as the remaining or outstanding balance declines III These percentages change over time because even though the total payment is constant the amount of interest paid each year is declining as the remaining or outstanding balance increases IV These percentages change over time because even though the total payment is constant the amount of interest paid each year is increasing as the remaining or outstanding balance increases V These percentages do not change over time interest and principal are each a constant percentage of the total payment

1 Show that I 2 1 2 Show that 2 1 2 n n 1 2 1 341 WIN 3 113

Given the indicated maturities listed in the following table assume the following yields for US Treasury securities Maturity Years 1 5 Yield 3 6 On the following graph plot the yield curve implied by these interest rates Place a blue point circle symbol at each maturity and interest rate in the table and the yield curve will draw itself INTEREST RATE Percent 10 9 8 7 0 10 20 30 5 5 5 5 4 2 4 0 10 15 20 25 30 MATURITY Years Yield Curve

Suppose the Federal Reserve the Fed decides to tighten credit by contracting the money supply Use the following graph by moving the black X to show what happens to the equilibrium level of borrowing and the new equilibrium interest rate INTEREST RATE r Percent 16 D CAPITAL Billions of dollars S2 Short term interest rates Which tend to be more volatile short or long term interest rates O Long term interest rates S1 Equilibrium If the inflation rate was 3 40 and the nominal interest rate was 5 60 over the last year what was the real rate of interest over the last year Faith etis average Round intermediate calculations to four decimal places

The following graph shows the supply of and demand for capital in a market over the last year You can see that the demand for capital has increased over the last year the demand curve shifted to the right Place the black X at the equilibrium interest rate and the quantity of capital INTEREST RATE r Percent 20 18 16 14 12 10 8 2 D2 D1 0 0 2 4 14 16 18 20 6 10 12 6 8 CAPITAL Billions of dollars Equilibrium The market interest rate increased by 2 0 and the amount of capital borrowed Which of the following factors could be responsible for the change in demand shown in the graph by The Federal Reserve the Fed decided to relax Its monetary policy and expanded the money supply O Expected inflation decreased billion

Everyone uses money and it is important to understand what factors affect the cost of money Consider the following scenario A friend comes to you and asks you to invest in his business instead of investing in Treasury bonds You think he has a good business model so you tell him you are willing to invest as long as the expected return on the investment is at least four times the return you would have received on the Treasury bonds Determine which of these fundamental factors is affecting the cost of money in the scenario described Time preferences for consumption Inflation Risk

For the given cost function C x 250 give at least 3 decimal places a The cost when producing 1850 items x 3375 b The average cost when producing 1850 items c The marginal cost when producing 1850 items e The minimal average cost find the following For average and marginal costs d The production level that will minimize the average cost per item per item per item items L

8 Identify the conic solve for y and graph using your calculator Find the angle of rotation write the unrotated equation in general form 2x 3 xy y 2x 3y 4 0 a Type Unrotated eqn Graph of rotated eqn y

Suppose that the growth rate of a tree is 0 514 feet per year What would be the growth rate in mm per day use 1 foot 304 8 mm and 1 day 365 25 days Your Answer

Complete the following chart to evaluate Marca s current budget then adjust monthly amounts to make a new budget such that each expense falls within the guidelines Expense Category Housing utilities Food Clothing Health Personal care Transportation Recreation Education Savings Miscellaneous Total Recommended of Net Monthly Income 27 33 20 26 3 5 12 14 6 8 6 10 12 18 Monthly Monthly Current Low High New Amount OK Amount 1000 985 125 500 250 100 300 100 New

24 G 1 25 26 A bag contains ten tiles labeled B C D E F G H I J and K One tile will be randomly picked What is the probability of picking a vowel Write your answer as a fraction 00 20 5 3

Elsa has a new aquarium The tank is in the shape of a rectangular prism 60 in long 24 in wide and 36 in deep She plans to raise fish and sell them to a local pet store The pet store will inspect the aquarium to make sure that the fish are being kept in a healthful environment One of the main concerns is that each fish has enough water Elsa looks up the amount of water needed for the species of fish she plans to raise She finds the answer but it is given in cubic feet a Find the volume of water that the tank holds in cubic feet Use the table of conversion facts as needed b The particular species Elsa plans to raise requires at least 0 42 ft of water per fish If there is any amount less than this no matter how much less the pet store will not accept Elsa s fish What is the largest whole number of fish that she can keep in the aquarium fish c The pet store will pay 1 79 for each fish If she fully populates her aquarium and sells all the fish how much money will she collect Conversion facts for length 12 inches in 3 feet ft 36 inches in I foot ft 1 yard yd I yard yd F B

24 25 26 27 X 28 8 X 0 0 3 29 8 a Rachel entered a raffle to win a movie ticket The probability that she wins a movie ticket is Find the odds in favor of her winning a movie ticket 11 0 to 5 30 31 b Eric is watching his favorite soccer team playing a match The odds against his favorite tearn winning are 10 tearn winning 0 32 33 34 35 What is the probability of his favorite

A runner s racecourse has a total distance of 2 5 mi Race officials want to mark the course every 200 yd with a flag including one at the finish line The starting line does not need a flag How many flags are needed First fill in the blanks on the left side of the equation using three of the ratios shown Then write your answer on the right side of the equation Ratios 200 yd 1 flag 2 5 mi 1 1 flag 200 yd 5280 ft 1 mi 1 mi 5280 ft 1 3 ft 1 yd 1 yd 3 ft 1 B flags ft yd in flag E

4 Evaluate express final answer in scientific notation 0 00012 0 000000013 G

6 Evaluate express final answer in scientific notation 0 028 14000 Answer

7 Evaluate express final answer in scientific notation 33 0 044

5 Evaluate express final answer in scientific notation 126904761 9048 0 41 x 0 00000063

There are 5 roses in a vase of 14 flowers The rest are daisies a What is the ratio of daisies to all flowers in the vase 0 b What is the ratio of daisies to roses 0 X

1 Evaluate express final answer in scientific notation 4 4 x 10 9 Answer

X not X b Subtract 1 P x 3 000 n 3 4 P X 3 00000 P not x 4 3 1 1 P X is the same as None of the above P X P not X 4 X 1 P not X None of the above c Select the answer that makes the sentence true S X X

2 3 0 4 01 4 19 a Keiko is at a charity fundraiser and has a chance of receiving a gift The odds in favor of receiving a gift are a gift Dla 6 ola 5 13 What are the odds against the box having a b A child has a box of candy which might have a toy inside The probability of the box having a toy is toy 18 0 0 0 Find the probability of Keiko receiving to

9 Write the following in scientific notation 758 000 Answer x

3 4 0 When ordering the Kids Lunch at Burger Universe the customer must choose a size whether or not to have cheese a type of bun a side order and a type of fruit drink Here are the possibilities for each choice Possibilities Choice Size Cheese Type of bun Side order Fruit drink How many Kids Lunches are possible 5 Small Medium Large With cheese Without cheese White bun Wheat bun Fries Onion rings Fruit cup Orange Grape Cherry Lemonade Mango X 6

1 2 0 3 4 5 A bag contains eleven balls labeled 1 through 11 One ball will be randomly picked What is the probability of picking a multiple of 3 Write your answer as a fraction 00 6

Using the information for Symbolic Electronics Inc presented in the table below determine the following 1 Lowest price paid for a share of the stock in the last 12 months 2 Highest price paid for a share of stock in the last 12 months 3 Percentage of change in the stock s price since the beginning of the year 7 Year to Date Change 52 Week Hi 52 Week Lo Dividend Yield Percentage 1 Lowest price paid 2 Highest price paid 3 Percentage of change pt 1 of Unlimited 1 56 EPS 53 88 PE Ratio 37 49 Volume 0 70 Close Price 1 51 Net Change O 0 X 1 81 25 67 1 460 000 46 46 0 85

Partially Correct Your answer is incorrect Profit on this stock transaction Your answer is incorrect During 2022 Jim Smith purchased 250 shares of common stock issued by Red Hot Food Processing for 4400 including commission Later in the same year JP sold the shares for 5000 after commission Calculate the following Round all answers to two decimal places 1 Profit on this stock transaction 2 Percentage return on investment 23 182 13 64

5 6 7 8 9 10 11 12 13 A restaurant manager is listing 10 items on a menu Of these menu items 8 are appetizers and 2 are main courses All of the appetizers will be listed before both of the main courses In how many ways can the restaurant manager list the items 0

Fully simplify the following expression There should be no negative exponents in your answer Show your steps to demonstrate your understanding of exponent laws x6x 2 y 6 2 y 2 z

years 8 5 9 10 11 X 12 Suppose that 2000 is placed in a savings account at an annual rate of 2 9 compounded quarterly Assuming that no withdrawals are made how long will it take for the account to grow to 2500 Do not round any intermediate computations and round your answer to the nearest hundredth If necessary refer to the list of financial formulas 13 X C Hel

1 Dividend per share of preferred stock 2 Dividend per share of common stock 17 0 18 X 19 3 20 On April 1 2022 the board of directors of Overload Spring Company voted to distribute 4 880 000 to the firm s stockholders If the firm has issued 200 000 shares of 6 preferred stock with a par value of 10 and 2 030 000 shares of common stock outstanding calculate the following Round all answers to the nearest cent 21 22 23

ities of draws with replacement A fair die is rolled 5 times What is the probability that a 2 is obtained on at least one of the rolls Round your answer to three decimal places 0 X S 0 5

For the following equation determine the values of the missing entries Reduce all fractions to lowest terms y x 2x 1 Note Each column in the table represents an ordered pair If multiple solutions exist you only need to identify one Answer

A tomato sauce company is shipping boxes containing 12 cans of their spaghetti sauce Each can is 9 cm in diameter and 9 cm tall Determine the surface area of the rectangular box that minimizes the amount of cardboard needed assume no overlaps

How many arrangements of 3 digits can be formed from the digits 0 through 9

Solve for a to 1 decimal place 10 ft 105 12 ft 40 X

The Siddiqi family takes out a 25 year mortgage for 416000 with monthly payments at 4 59 a compounded semi annually At the end of their first 5 year term they renew their mortgage at 4 34 a compounded semi annually What is their outstanding balance when they renew

Your friend is starting a new job and they have to choose between two salary agreement options Both job start at 55000 in year 1 and with option A the yearly pay increases by 4000 year while option B is an annual increase of 7 each year a Complete each table of values b Classify each option as linear quadratic exponential or none of these and finally c Advise your friend as to which is the better option depending on their long term plans

Stonewall Exteriors is pouring concrete for a fountain they are installing They need concrete for the circular wall as well as the floor underneath both of which must be 5 in thick If the outer diameter of the pool is 20 ft and the walls are 50 cm high calculate the cost of the concrete if it can be delivered for 137 yd

Fill in the blanks in the following difference table X 2 1 0 1 2 y 5 13 7 11 6 6 6

Die 3 A 25000 loan is to be paid off over 5 years with bi weekly payments If the interest rate is 3 00 a compounded bi weekly calculate the total amount of interest paid to the bank

If Angela were to paint her living room alone it would take 5 hours Her sister Fran could do the job in 7 hours How many hours would it take them working together Express your answer as a fraction reduced to lowest terms if needed

Solve the following exponential equation using the common base method 8 4 6 32x

Solve AABC if 7 cm b 7 cm b 8 3 cm and c 9 2 cm

The square based pyramid shown has a volume of 576 cm Determine the slant height x to 1 decimal place X

Rewrite the following expression as a fraction involving powers with only positive exponents then evaluate no decimals Show your steps 2 x 2 7 2 3 37

1 point Which of the following graphs are connected N M 0 N DA C I 0 P H L H D E K N B D C F 0 I B bl