Math week 4 Please see attached

MM255 Business Math and Statistical Measures

Unit 4: Instructor Graded Assignment Simple Interest In this and future Instructor Graded Assignments, you will be asked to use the answers you found in the Unit 1 Assignment. Note: For these questions you need to cite a reliable source for information, which means you cannot use sites like Wikipedia, Ask.com®, and Yahoo® answers. If you do use those sites the instructor may award 0 points for your response. TheAssignment problems must have the work shown at all times. The steps for solving the problems must be explained. Failure to do so could result in your submission being given a 0. If you have any questions about how much work to show, please contact your instructor. Assignments must be submitted as a Microsoft Word®document and uploaded to the Dropbox for Unit 4. Please type all answers directly in this Assignment below the question it applies to. All Assignments are due by Tuesday at 11:59 PM ET of the assigned Unit. Note: All interest rates are to be assumed to be yearly interest rates. In these questions, you will need to use the date that unit 4 starts for your class. List the date that Unit 4 started for your class:

 Unit 4 start date: For this example, we will use 4/30/2013 as our date. Also, now we will be working totally different questions using the same idea as your project questions. As such, we will not be using different colors to distinquish the questions anymore.

Example Question 1: You take out a simple interest loan for $2000 at 10% yearly interest on the date unit 4 starts for you. If you repay the loan on December 15th... a) How much interest do you pay? 1a Example Solution: To solve this you need to first calculate how many days you had the loan out for. Using the table in your book (in the 10th edition it is on page 396), you will see that November 4th is the 308th day of the year, and December 15th is the 349th day of the year. Therefore, you had the loan 349 - 308 = 41 days. Now, putting that into the simple interest formula A = P(1 + rt) will give you:

A = 2000 * (1 + .1 * (

)) = $2022.47 total that you need to repay

MM255 Business Math and Statistical Measures

b) How much do you pay in interest? 1b Example Solution: When one repays a loan, anything that you pay over the original amount borrowed is interest. Since we borrowed $2000 and we paid back $2022.47, that means that we paid: 2022.47 - 2000 = $22.47 in interest.

Example for Question 2: You decide to take out a $15000 simple interest loan at 5%, on the date unit 4 started for you. a) In 30 days, you decide to pay off $5000. What is your new principal? 2a Example Solution: To solve this you need to first figure out how much was due when you made the payment. We made the payment 30 days after we took out the loan, so we owed on that date:

A = 15000 ( 1 + .05*(

)) = $15061.64

We paid 5000 of that, so we still owe: $15061.64 - $5000 = $10061.64, which is our new prinicpal. b) After 75 more days pass, you decide to pay another $5000. What is your new principal? 2b Example Solution: Just like in part 2a, we need to calculate how much we owed when we made this payment. However, we will be using our answer in 2a, as that is the new balance as of when the 75 days start. Therefore, using the simple interest formula, we get:

A = 10061.64 * (1 + (.05) * (

) = $10165.01 is our new balance when we make this payment.

We pay another $5000 then, so the total we owe now is $10165.01 - $5000 = $5165.01, which is our new principal. c) After 180 more days pass the entire loan comes due. How much do you owe? 2c Example Solution: Just like in parts 2a and 2b, we need to use the simple interest formula to calculate how much is due. Using the formula and applying it to our balance from 2b gives us:

A = $5165.01 * (1 + (.05) * (

= $5292.37, which is the balance due at this point in time.

MM255 Business Math and Statistical Measures

Example Question 3: You need $250 badly and decide to write a check at a check cashing place to get the money. You write the check for $350 and the check is going to be cashed in 3 weeks. What simple interest rate did you pay? 3 Example Solution: For this problem, you know the future value and the amount borrowed, but you do not know the interest rate. To solve this, plug what you know into the equation for simple interest. Doing that will give you:

350 = 250 (1 + r (

Now we need to solve this for r. Divide both sides by 250 to get:

1.4 = 1 +

Now we will subtract one from both sides, giving us

0.4 =

Multiply by 52 to cancel the fraction, and we get: 20.8 = 3r Finish by dividing by 3 6.93..... = r However, r is in decimal form, and if we convert that to a percent, we will get 693.33% was the yearly interest rate (and our final answer).