Calculating Interest in the Real World Project

Transcription

1 Name: Due Date: Background Learn the Lingo: Calculating Interest in the Real World Project Interest the amount of money paid for the use of money. (If you are borrowing money, you pay interest to the bank/lender.) (If you are investing, you collect interest from the bank.) Principal the initial value of the account Rate of Interest Amount charged for use of the principal for a given period of time, usually given as a yearly (per annum) percent. Compounding When the interest earned in the account is added to the value of the account. After compounding, the interest is found based on this new account value until the next compounding. Interest is commonly compounded Annually 1 time per year; n=1 Monthly 12 times per year; n = 12 Semi-annually 2 times per year; n = 2 Weekly 52 times per year; n = 52 Quarterly 4 times per year; n = 4 Daily 365 times per year; n = 365 Compound Interest Formula Used to find the future value in an account after a certain period of time nt r A P 1 n where A = amount after time w/ interest P = principal r = interest rate written as a decimal (Divide % by 100 if you need help converting) n = number of times compounding per year t = number of years Continuous Compounding Formula Used to find the future value in an account if interested is continuously added to present value of the account. rt A Pe where A = amount after time w/ interest P = principal r = interest rate written as a decimal t = number of years Recursive Sequence Formula r An new amount An 1 Previous Amount An 1 An 1 P n r interest rate n compounding P monthly payment

2 Monthly Car Payment Formula nt r r 1 n n A P nt r 1 1 n A Monthly Payment P Principal r interest rate as decimal n compounding t time in years for loan Timeline Day 1: Research and begin computations Day 2: and begin Google Presentation. Day 3: Continue computations & compile info on Google Presentation. Day 4: Finishing touches on Google Presentation and assign roles for presentation. Day 5: Present results with all members present. (Project officially due today!) Day 6: Finish presentations if needed & reflect on new insights gained from project & presentations. Grouping and Presentations Each group will consist of 3-4 members. No more, no less. Each partner is required to contribute their fair-share of the work. This does not mean what you feel is fair, but what the group feels is fair and that the work is divided up equally by all of the group members. Each group member will present a section of the project. This is not optional. Links You may use your existing bank/credit union OR look up another financial institution this link may be of help in finding one: Earning Interest from a Financial Institution You will research savings accounts and determine how much money you will collect by investing. Let s make some money! Owing the Financial Institution There are many occasions that arise when we need to borrow money from a financial institution and are charged an interest rate on the amount borrowed. You will determine how much you owe the bank after a given period of time. Amortization Tables Making Payments Create an amortization table for your scenarios. These tables need to be placed into your presentations. We will go through how to create a recursive function for this as a class. You will apply it to your specific rates once you find the institution of your choosing. REMINDER: COMPUTATIONS = SHOW YOUR WORK FOR CREDIT

3 Part A: Savings Accounts Earning Interest You are going to invest $1,000 into a savings account and want to know how much interest you will have earned after 6 months, after 1 year, and after 5 years. a) Find a savings account through a financial institution of your choosing. b) Identify the financial institution, the AYP/APR (interest rate) offered for your investment of $1,000 and use monthly compounding for that account unless otherwise specified on the website. c) Compute the value of your account after each period of time show your work! d) Determine the amount of interest earned over each time period show your work! e) How long will it take to double your investment? (Brace yourself this is not a pretty number!) f) Reflection: What have you learned about savings accounts? What recommendations would you have for someone interested in opening a savings account? Part B: CDs Another option when saving money is to put your money in a CD (Certificate of Deposit). For a CD, you give the bank the right to hold onto your money for a certain period of time on the condition that it pays you a certain amount of interest at the end of that period of time. The disadvantage of a CD is that you do not have access to your money for the term of the CD but the advantage is that the interest rates offered for CDs are usually significantly higher than those offered on savings accounts. a) Find a rate for a 6 month, 1 year and 5 year CD through a financial institution of your choosing. b) Identify the financial institution, the interest rate(s) offered for your investment of $1000 and the level of compounding used for that account. c) Compute the value of your account when the CD matures (after 6 months, 1 year & 5 years respectively.) Show your work! d) Determine the amount of interest earned over each time period show your work! e) How long will it take to double your investment? f) Reflection: What have you learned about CDs? What recommendations would you have for someone interested in opening a CD? Comparison of Savings & CD Accounts Reflection comparing and contrasting parts A and B required Reflection: How would you invest your money in this institution? Would you use a savings account or a CD? Explain your decision in detail, listing at least one advantage and one disadvantage of the type of account you choose. Part C: Charging on a Credit Card So you just didn t have quite enough cash to cover those must-have purchases and out came that little plastic card filled with free money right? Ok maybe not so much free and maybe it was necessary, but let s see what you ll end up paying for the $5,000 of credit card debt you managed to rack up. a) Find an interest rate for a credit card from a financial institution of your choosing. b) Identify the financial institution, the interest rate charged and the level of compounding used for that account. c) Most credit cards have a minimum payment required each month. For this scenario, please use a minimum payment of $ per month. Create a recursive function to represent this situation & include this formula in your presentation. Now use the Amortization Table on the

4 excel spreadsheet provided on my teacher webpage to see the overall trend of payments and amounts owed. (Include your Amortization Table in your presentation as well.) 1. Determine how much you have paid after 1 year. 2. Determine how much you would owe after 1 year, making the minimum payment listed above. 3. Determine how much total interest you paid after 1 year. i. Step 1: Subtract the amount owed from the initial amount. ii. Step 2: Subtract the difference found in (i) from the amount paid after 1 yr. This is the total amount of interest you paid. 4. Determine how long it will take to pay off your debt & how much you will pay overall. d) How do these amounts change if you could afford to pay $300/month? Create another recursive formula & Amortization Table to compute the amount paid, amount owed and amount of interest paid after 1 year. e) Make summary statements comparing the amounts you found in (c) to those in (d). What are the benefits and drawbacks of (c) and (d)? f) What if you make no payments? Compute the amount you end up paying for your purchases if left for 1 year, 5 years or 10 years. Note: Use the compound interest formula. g) Determine the amount of interest paid over each time period from part (f). h) Reflection: Would you choose this financial institution as your credit card provider? Why or why not? Explain your decision in detail. List two factors you need to consider when choosing your credit card provider. Part D: Buying Your Dream Car Find the amount you will end up paying for your car if you pay off your car in 3 years vs. paying your car off in 5 years. The interest rate may vary based on the length of your loan. a) Find the price for your dream car and record the type of car including make, model & year. b) Find a rate for a car loan through a financial institution of your choosing. Some banks have different rates for used or new car loans. If this is the case, base your decision on if your dream car would be new or used. c) Identify the financial institution, the interest rate offered for your loan and the level of compounding used for that account. d) Determine the monthly payment for your car with the given interest rate for both 3 & 5 years. If a 3 year rate is not listed for your institution, use 4 or the year rate listed. e) Compute the amount paid for your car if paying it off in 3 years vs. paying it off in 5 years. f) Determine the amount of interest paid over each time period. g) Reflection: How s your dream car looking now? Explain your decision in detail. List two factors you need to consider when purchasing a car. Part E: The Presentation Every member of your group must be actively involved in explaining the different components of your project. Your presentation format must include information about the financial institution you selected, all of the computations, results of your computations and some overall reflections on each of the four types of accounts you examined in your research. You may include any additional information you see fit get creative!

5 Rubric: Calculating Interest in the Real World Project Max Points Points Received Comments 1. Part A: Savings Account 21 Financial Institution Info. 1 Interest Rate 1 ($1000) Value of 6 months 2 Value of 1 yr 2 Value of 5 yr 2 ($1000) Interest 6 months 1 Interest 1 yr 1 Interest 5 yr 1 Double Investment 4 Reflection 6 2. Part B: CDs 27 Financial Institution Info. 1 Interest Rate 1 Value of 6 months 2 Value of 1 yr 2 Value of 5 yr 2 Interest 6 months 1 Interest 1 yr 1 Interest 5 yr 1 Double Investment 4 Reflection 6 Comparison: Savings vs CD 6 3. Part C: Credit Card 41 Financial Institution Info 1 Interest Rate 1 : Min. Payment $125 Recursive Sequence 2 Amortization Table for $125 2 Amount Paid After 1 yr 1 Amount Owed After 1 yr 1 Amount of Interest Paid 1 yr 1 Payoff Time & Amount 2 : Min. Payment $300 Recursive Sequence 2 Amortization Table for $300 2 Amount Paid After 1 yr 1 Amount Owed After 1 yr 1 Amount of Interest Paid 1 yr 1 Payoff Time & Amount 2 Comparison of Minimum Payments 6 No Payments Total Amount 1 yr 2 Total Amount 5 yr 2 Total Amount 10 yr 2 No Payments Total Interest 1 yr 1 Total Interest 5 yr 1 Total Interest 10 yr 1

6 Reflection 6 4. Part D: Buying a Car 21 Dream Car Price, Make & Model 2 Financial Institution Info 1 Interest Rate for 3 yr 1 Interest Rate for 5 yr 1 Monthly Payment for 3 yr 2 Monthly Payment for 5 yr 2 Payoff in 3 yrs. 2 Payoff in 5 yrs. 2 Interest in 3 yrs. 1 Interest in 5 yrs. 1 Reflection 6 5. Part E: Presentation 40 Neat and Organized 10 Verbal Accuracy (What s said) 20 Eye Contact, Projection, body 5 language Fluidity (Smoothness) 5 Extra Credit 10 Creativity and Originality 5 Professional Attire 5 GRAND TOTAL 150 Additional Comments: