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The Fibonacci numbers
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- When you borrow money to buy a house, a car, or for some other purpose, you repay the loan by making periodic payments over a certain period of time. Of course, the lending company will charge interest on the loan. Every periodic payment consists of the interest on the loan and the payment toward the principal amount. To be specific, suppose that you borrow $1,000 at an interest rate of 7.2% per year and the payments are monthly. Suppose that your monthly payment is $25. Now, the interest is 7.2% per year and the payments are monthly, so the interest rate per month is 7.2/12 = 0.6%. The first months interest on $1,000 is 1000 0.006 = 6. Because the payment is $25 and the interest for the first month is $6, the payment toward the principal amount is 25 6 = 19. This means after making the first payment, the loan amount is 1,000 19 = 981. For the second payment, the interest is calculated on $981. So the interest for the second month is 981 0.006 = 5.886, that is, approximately $5.89. This implies that the payment toward the principal is 25 5.89 = 19.11 and the remaining balance after the second payment is 981 19.11 = 961.89. This process is repeated until the loan is paid. Write a program that accepts as input the loan amount, the interest rate per year, and the monthly payment. (Enter the interest rate as a percentage. For example, if the interest rate is 7.2% per year, then enter 7.2.) The program then outputs the number of months it would take to repay the loan. (Note that if the monthly payment is less than the first months interest, then after each payment, the loan amount will increase. In this case, the program must warn the borrower that the monthly payment is too low, and with this monthly payment, the loan amount could not be repaid.)arrow_forwardWhen you use a mortgage to purchase a home, the lending institution effectively owns the home. You buy back part ownership in the home with each monthly payment. The part you have bought back is your equity in the home. If the mortgage amount is P dollars, the monthly interest rate is r as a decimal, and the term of the mortgage is t months, then your equity after k payments is E(k) = P((1 + r)k − 1) (1 + r)t − 1 dollars. In this exercise, assume that the mortgage amount is $200,000, the APR is 6% so r = .06/12 and the term of the loan is 30 years (360 months). (a) Find a formula for the equity. (b) Make a graph of the equity over 360 months, the term of the loan. (c) Does the graph show that you have half-ownership in the home halfway through the term of the mortgage? Halfway through the term of the mortgage corresponds to k1 = _______ payments. From the graph, we see that E(k1) is ________ half of the mortgage amount, so we _______ have half-ownership in the home…arrow_forwardSuppose you have a certain amount of money in a savings account that earns compoundmonthly interest, and you want to calculate the amount that you will have after a specificnumber of months. The formula is as follows: F=P×(1+i)tF=P×(1+i)t The terms in the formula are: • F is the future value of the account after the specified time period.• P is the present value of the account.• i is the monthly interest rate.• t is the number of months.• F is the future value of the account after the specified time period.• P is the present value of the account.• i is the monthly interest rate.• t is the number of months. $$ Write a program that prompts the user to enter the account’s present value, monthly interest rate, and the number of months that the money will be left in the account. The program should pass these values to a function that returns the future value of the account, after the specified number of months. The program should display the account’s future value.arrow_forward
- In the real world, functions are mathematical representations of input-output situations. A vending machine is one such example. The input is the money combined with the selected button. The output is the product. Here is another example: The formula for converting a temperature from Fahrenheit to Celsius is a function expressed as: C = (5/9)*(F - 32), where F is the Fahrenheit temperature and C is the Celsius temperature. If it is 77 degrees Fahrenheit in Phoenix Arizona, then what is the equivalent temperature on the Celsius thermometer? Our input is 77. C = (5/9)*(77 - 32) C = (5/9)*(45) C = 25 The equivalent temperature is 25 degrees Celsius. To complete the Discussion activity, please do the following: Choose your own function or choose from the list below and then provide a unique example of a function and evaluate the function for a specific input (like the example above). Arm length is a function of height. The circumference of a circle is a function of diameter. The height of…arrow_forwardA fish-finder is a device used by anglers to find fish in a lake. If the fish-finder finds a fish, it will sound an alarm. It uses depth readings to determine whether to sound an alarm. For our purposes, the fish-finder will decide that a fish is swimming past if:there are four consecutive depth readings which form a strictly increasing sequence (such as 3 4 7 9) (which we will call "Fish Rising"), orthere are four consecutive depth readings which form a strictly decreasing sequence (such as 9 6 5 2) (which we will call "Fish Diving"), orthere are four consecutive depth readings which are identical (which we will call "Constant Depth").All other readings will be considered random noise or debris, which we will call "No Fish."Create a Python program called "fishfinder_firstname_lastname" that takes 1 input of string of 4 numbers separated with comma. Your program must display "Fish Rising", "Fish Diving.", "Fish At Constant Depth" or "No Fish".Example:30,10,20,20 Must display No…arrow_forwardOpen notes and open book. Suppose you have a certain amount of money in a savings account that earnscompound monthly interest, and you want to calculate the amount that you willhave after a specific number of months. The formula is as follows:f = p * (1 + i)^t• f is the future value of the account after the specified time period.• p is the present value of the account.• i is the monthly interest rate.• t is the number of months.Write a program that takes the account's present value, monthly interest rate,and the number of months that the money will be left in the account as threeinputs from the user. The program should pass these values to a function thatreturns the future value of the account after the specified number of months.the program should print the account's future value.arrow_forward
- This must be done using CORAL language. Primary U.S. interstate highways are numbered 1-99. Odd numbers (like the 5 or 95) go north/south, and evens (like the 10 or 90) go east/west. Auxiliary highways are numbered 100-999, and service the primary highway indicated by the rightmost two digits. Thus, the 405 services the 5, and the 290 services the 90. Given a highway number, indicate whether it is a primary or auxiliary highway. If auxiliary, indicate what primary highway it serves. Also indicate if the (primary) highway runs north/south or east/west. Ex: If the input is: 90 the output is: The 90 is primary, going east/west. Ex: If the input is: 290 the output is: The 290 is auxiliary, serving the 90, going east/west. Ex: If the input is: 0 or any number not between 1 and 999, the output is: 0 is not a valid interstate highway number.arrow_forwardDuring Eid, it is a tradition for every father to give his children money to spend on entertainment. Chef has N coins; denote the value of the coin i by vi. Since today is Eid, Chef gives one coin to each of his two children. He wants the absolute value of the difference between the values of the coins given to the two children to be as small as possible to be as fair as possible. Help the chef by telling him the minimum possible difference between the values of the coins given to the two children. Of course, the chef cannot give the same coin to both children. Note: Please answer in python only Possible input 1 3 142 Required Output 1arrow_forwardDuring Eid, it is a tradition for every father to give his children money to spend on entertainment. Chef has N coins; denote the value of the coin i by vi. Since today is Eid, Chef gives one coin to each of his two children. He wants the absolute value of the difference between the values of the coins given to the two children to be as small as possible to be as fair as possible. Help the chef by telling him the minimum possible difference between the values of the coins given to the two children. Of course, the chef cannot give the same coin to both children. Note: Please answer in C++ Programming language. Possible input 1 3 142 Required Output 1arrow_forward
- A basic safe type of investment is an annuity: one makes monthly deposits of size P for n months at a fixed annual interest rate r, and at maturity collects the amount 12P n r ((₁ + 2)² − ¹) 12 r (This is not the definition of annuity that you may be familiar with, but the calculation is part of any accumulation of funds over time.) Say you want to create an annuity for a term of 300 months and final value of 1,000,000 dollars. Using nlsolve, make a table of the interest rate you will need to get for each of the different contribution values P 500 + 50k, k = 0, ..., 10. - Hint: if you write a function for the value of annuity, or the difference between this value and one million dollars with several arguments (P, r, n), you can then create a new function of just the one variabler for each value of P in a loop. The table and pretty tables approach used in homework 2 will be helpful here.arrow_forwardI am what you call a perfectionist. I always strive for perfection, and I appreciate everyone and everything that is perfect. That is why I have recently acquired an appreciation for perfect numbers! I absolutely need to know which numbers from 1 to 1000 are considered perfect. From what I recall, a perfect number is a positive integer that is equal to the sum of all its divisors other than itself. Example: 6 is a perfect number because the divisors of 6 other than itself are 1, 2, and 3, and 1 + 2 + 3 = 6. c++ codearrow_forwardOne hundred tickets, numbered 1, 2, 3, . . . , 100, are sold to 100 different people for a drawing.Four different prizes are awarded, including a grand prize. How many ways are there to awardthe prizes if:a) the person holding ticket 35 wins the grand prize?b) the person holding ticket 64 wins one of the prizes?c) the person holding ticket 18 does not win a prize?d) the people holding tickets 30 and 50 both win prizes?arrow_forward
- C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage LearningC++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr