Concept explainers
The following information is available for a bank account:
Date | Deposits | Withdrawals | Interest | Balance |
5/1 | 1522.33 | |||
220.13 | 327.26 | |||
6/1 | ||||
216.80 | 378.51 | |||
7/1 | ||||
450.35 | 106.80 | |||
8/1 | ||||
127.31 | 350.61 | |||
9/1 |
Note that the money earns interest which is computed as
Interest
where
(a) Use the conservation of cash to compute the balance on 6/1, 7/1, 8/1, and 9/1 if theinterest rate is 1% per month
(b) Write a differential equation for the cash balance in the form
where
For this case, assume that interest is compounded continuously; that is, interest
(c) Use Euler's method with a time step of 0.5 month to simulate the balance. Assume that the deposits and withdrawals are applied uniformly over the month.
(d) Develop a plot of balance versus time for(a) and (c).
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Numerical Methods for Engineers
Additional Math Textbook Solutions
Advanced Engineering Mathematics
Basic Technical Mathematics
Fundamentals of Differential Equations (9th Edition)
A First Course in Probability
- The following list gives the gross federal debt(in millions of dollars) for the U.S. every 5 years from 1945 to 2000: Year Gross Federal Debt ($millions) 1945 260,123 1950 256,853 1955 274,366 1960 290,525 1965 322,318 1970 380,921 1975 541,925 1980 909,050 1985 1,817,521 1990 3,206,564 1995 4,921,005 2000 5,686,338 Construct a scatter plot with this data. Do you observe a trend? If so, what type of trend do you observe? Use Excel to fit a linear trend and an exponential trend to the data. Display the models and their respective r^2. Interpret both models. Which model seems to be more approprate and why?arrow_forwardThe APR for loans can also be approximated (however, not within the 1 4 of 1% accuracy required by Regulation Z†) by using the following formula: APR = 2mI P(n + 1) where m = the number of payment periods per year I = the interest (or finance charge) P = the principal (amount financed) n = the number of periodic payments to be made. Thus, if m = 12, I = $264, P = $1200 and n = 30, APR = 2mI P(n + 1) = 2 × 12 × 264 1200 × 31 = 17%. Use the APR formula to find the APR to one decimal place. (Assume m = 12.) AmountFinanced FinanceCharge Number ofPayments $4000 $332 12 %State the difference between the answer obtained by the formula and the answer obtained using the True Annual Interest Rate (APR) table. (Round your answer to one decimal place.) %arrow_forwardThe following data represent the exchange rates for Currency A in terms of Currency B for 14 months. Complete parts a through e below. 0.66 0.71 0.93 1.14 1.42 0.95 0.77 0.59 1.51 0.59 0.55 0.86 1.40 0.90arrow_forward
- Apply the EOQ model to the following quantity discount situation in which D = 530 units per year, Co = $43, and the annual holding cost rate is 30%. DiscountCategory Order Size Discount(%) Unit Cost 1 0 to 99 0 $12.00 2 100 or more 4 $11.52 What order quantity do you recommend? If required, round your answer to the nearest whole number.arrow_forwardBelow are the tax rates for NZ for the 2023 - 2024 tax year. Income Tax Rate $0 - $14,000 10.5% $14,001 - $48,000 17.5% $48,001 - $70,000 30% $70,001 - $180,000 33% $180,001 + 39% So, if for example, a person earned $20,000 per annum, the first $14,000 would be taxed at 10.5%, and then the remaining $6000 would be taxed at 17.5%, giving a tax bill of $14,000 × .105 + $6,000 × .175 = $2,520. (a) Use the information above to write a piecewise function that takes as input the amount a person earns in a year and outputs the amount of tax they pay over the year. (b) Use your answer from (a) to calculate how much tax a person would pay if they are earning $80,000 per year.arrow_forwardThe following data were taken from Miller Company's balance sheet: Dec. 31, Year 2 Dec. 31, Year 1 Total liabilities $150,000 $105,000 Total stockholders' equity 75,000 60,000 a. Compute the ratio of liabilities to stockholders' equity. Round your answers to one decimal place. Liabilities toStockholders' Equity 12/31/Year 2: fill in the blank 1 12/31/Year 1: fill in the blank 2 b. Has the creditors' risk increased or decreased from December 31, Year 1, to December 31, Year 2?arrow_forward
- Apply the EOQ model to the following quantity discount situation in which D = 530 units per year, Co = $43, and the annual holding cost rate is 30%. DiscountCategory Order Size Discount(%) Unit Cost 1 0 to 99 0 $12.00 2 100 or more 4 $11.52 What order quantity do you recommend? If required, round your answer to the nearest whole number. fill in the blank 1arrow_forwardCompute Darryl's total Social Security and Medicare taxes for the third quarter, if she is self-employed and earns $1,220.00 on a weekly basis. a $186.66 b $1,213.29 c $1,308.45 d $2,426.58arrow_forwardThe following table reports prices and usage quantities for two items in 2009 and 2011. (Round your answers to the nearest integer.) Quantity Unit Price ($) Item 2009 2011 2009 2011 A 1,500 1,800 7.50 7.55 B 2 1 650.00 1,500.00 (a) Compute price relatives for each item in 2011 using 2009 as the base period. Item Price Relative A ? B ? (b)Compute an unweighted aggregate price index for the two items in 2011 using 2009 as the base period. I2011 = ?? (c)Compute a weighted aggregate price index for the two items using the Laspeyres method using 2009 as the base period. I2011 = ?? (d)Compute a weighted aggregate price index for the two items using the Paasche method using 2009 as the base period. I2011 = ??arrow_forward
- 10 The observed insurance policy deviates from the predicted policy, on average, by _______ ($1,000) a 44.465 b 49.406 c 54.895 d 60.994arrow_forwardThe Moneybuilder account offered by a chartered bank calculates interest daily based on the daily closing balance as follows: Interest rate (%) Amount to which the rate applies 0.00 Balance when it is below $1000 1.25 Entire balance when it is between $1000 and $3000 1.75 Portion of balance above $3000 The balance at the beginning of March was $1678. On March 5, $700 was withdrawn. Then $2500 was deposited on March 15, and $900 was withdrawn on March 23. What interest will be credited to the account for the month of March? (Do not round the intermediate calculations. Round your answer to the nearest cent.)arrow_forwardThe following data are taken from recent financial statements of Nike, Inc. (NKE) (in millions): Year 2 Year 1 Revenues (sales) $32,376 $30,601 Operating income 4,502 4,175 a. Determine the amount of change (in millions) and percent of change in operating income from Year 1 to Year 2. Round to one decimal place. Operating income $fill in the blank 1 fill in the blank 2% b. Determine the percentage relationship between operating income and sales for Year 2 and Year 1. Round to one decimal place. Year 1 fill in the blank Year 2 fill in the blankarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,