Question

MATLAB WORK PLEASE

Interest is accrued according to the following formula: A=P i(1 + i)" (1 + i)" – 1 where A is the annual payment, P is the present worth, i is the interest rate (not in percent), and n is the number of years. You decide to buy a $35,000 vehicle (P), but because you don't currently have the money to finance the entirety of the vehicle, you agree to pay $8,500 per year (A) for 7 years (n). Write a function which calculates the interest rate, i, using MATLAB's fzero command. Hint: Again, interest in not a percentage! For example, i = 0.5 = 50%. Plot f(i) vs. i and choose an "initial guess" Xo near the root (i.e. from the graphical method, determine an appropriate value for the initial guess xo). Function C Reset D MATLAB Documentation 1 function i = InterestRate(A,P,n) 2 % Inputs: 3 % A: annual payment (scalar) 4 % P: present worth (scalar) 5 % n: number of years (scalar) 6 % 7 % Output: 8 % i: interest rate (scalar) 9 % 10 % Write your code below: 11 12

Answer 1

Plotting the function outputs a curve like this

104 15 | 0.5 -0.5上 -0.3 -0.2 01 0 01 10.2 0.3 04 0.5

From here we see that the initial guess x0 can be set at 0.2

I have provided both the text and the screenshot for your better understanding. The screenshot also has some comments for your help. Please note that these are script files which are to be saved as "function_name.m" in your MATLAB root directory.

InterestRate.m

function i = InterestRate(A,P,n)

%declaring the function as y - f(i) = 0
fun = @(x) (A - P*((x*power(1+x,n))/(power(1+x,n) - 1)));

%using fzero and predetermined initial value to determine the root
i = fzero(fun,0.2);

end

OUTPUT

x Workspace Command Window Editor - InterestRate.m pilot.m InterestRate.m function i = InterestRate (A,P,n) 1 2 $declaring the function as y - f(i) = 0 fun = @(x) (A - P*((x*power (1+x, n))/(power (1+x, n) - 1))); >> A = 8500; P = 35000; n = 7; >> i = InterestRate (A,P,n) Interest rate is 0.15. i = 0.1535 fx >>| 4 5 fusing fzero and predetermined initial value to determine the root i = fzero (fun, 0.2); 7 end

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