What did I do wrong in my 'for' loop function?

The question is

With the help of an RESP (Registered Education Savings Plan), a parent can start putting aside money for a child's post-secondary education. Suppose that a young couple deposits $2,000 to start the savings plan, and each month thereafter they contribute $200. Assume that a fixed interested rate of 6.25% per year compounded monthly is applied.

Each month the balance increases according to the following formula: New balance = Old balance + (Old balance * Monthly interest rate) + Monthly contribution

nb(1) = 2000; %the initial balance
mir = 0.0625/12; %monthly rate
mc = 200;% contribution for each month
for B = 2 : 216
    nb(B) = (nb(B-1)+1) + ((nb(B-1)+1) * mir) + mc;
end
fprintf('At the end of 18 years you will have saved $ %.2f \n',nb(B))

when you run this, you will get 85431.77, But the correct answer should be 85035.09.

Where did I do wrong?

Answer 1

[Steven Lord]

In this line of your code:

    nb(B) = (nb(B-1)+1) + ((nb(B-1)+1) * mir) + mc;

What's the old balance? Are you certain that you're accurately carrying over the balance from the previous month into the calculations for the next month? [From the fact that I'm asking these questions, you're probably guessing the answer to that second question is no.]

[Minhao Wang]

the old balance(the initial balance) is 2000$ , I don't know where did I do wrong...

[Steven Lord]

If your initial balance nb(1) is 2000, when you go to compute the balance for month 2 nb(2) you start with an old balance of 2001. That may not seem like a big difference, but it's big enough compounded over two years to make your answer incorrect by about $400.

Answer 2

[Image Analyst]

Why are you adding 1 to the old balance nb(B-1)???

[Minhao Wang]

I thought that means add a month?

[Image Analyst]

No. B is the month, and the for loop takes care of incrementing the month number. You were improperly adding $1 to the old balance so that's why your answer was more than the correct answer.