Problem 1 : If a regular fixed payment P is made n times a year to repay a loan of amount A over a period of k years, where the nominal annual interest rate is r, P is given by
P = 𝑟𝐴(1 + 𝑟/𝑛)𝑛𝑘
𝑛[(1 + 𝑟)𝑛𝑘 − 1] 𝑛
You need to generate a table of repayments for a loan of $1000 over 15, 20, and 25 years, at interest rates that vary from 10% to 20% per annum in steps of 1%. (Tip: The table has 11 rows and 3 columns, with rows representing different interest rates and columns representing different years, n = 12). You need to use two different methods, the first is to use nested for loops, and the second is to vectorize the outer loop. You might use repmat(). The generated table is as follows:
10.7461 9.6502 9.0870
11.3660 10.3219 9.8011
12.0017 11.0109 10.5322
12.6524 11.7158 11.2784
13.3174 12.4352 12.0376
13.9959 13.1679 12.8083
14.6870 13.9126 13.5889
15.3900 14.6680 14.3780
16.1042 15.4331 15.1743
16.8288 16.2068 15.9768
17.5630 16.9882 16.7845
Problem 2 : Narcissistic number is a three-digit number, the sum of the third power of the digits in each bit of which is equal to itself (for example, 153 = 13 + 53 + 33). You may find more information by searching ” Narcissistic number “. You need to write two functions, one for finding all the narcissistic numbers and one for determining whether a three-digit number is a narcissistic number. The second function should be nested within the first function.
Problem 3: Consider the following 3 x 3 matrix: A=
132 846 795
Use array subscripts or MATLAB functions to create the following arrays from A – no decisions, loops, etc. Each array should be created using only a single statement.
i) B = 13
79 ii) C =
18
73 iii) D =
132
846
iv) Find the maximum value of each row
E=
3
8
9 v) F =
10807 00000 30409 00000 20605
Problem 4 [20]: Around 300 B.C. Euclid developed a wonderfully simple algorithm for determining the greatest common divisor of two positive integers. Please search online for “Euclidean Algorithm” to find out the details. Your job is to implement the following two functions:
1) function out=my_gcd(a,b)
which computes the greatest common divisor of two positive integers a and b. You may find the MATLAB function rem() useful.
2) function out=my_lcm(a,b)
which computes the least common multiple of two positive integers a and b. This can be computed in part using my_gcd.
Make sure you account for the case where a and/or b is zero in your my_gcd function. You can check this behavior by entering gcd(0,2), gcd(2,0), and gcd(0,0) into the MATLAB command line. Note that the least common multiple of a=0 or b=0 is not defined (only least common multiples of a and b larger than 0 should be returned).
You can compare your implementations to MATLAB’s built-in gcd and lcm functions to determine if everything is working correctly.
Problem 5 [20]: Given a string of ‘1’ and ‘0’, find the maximum number of consecutive times of ‘1’. Write a function to do this. Your function declaration should be as follows.
The sample is:
function y = lengthOnes(x)
x = ‘110100111’ y=3
