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Math Help - Problem breakdown (interest)

  1. #1
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    Problem breakdown (interest)

    There are a lot of stuff in this question... and I can't wrap my brain around it all. How do I break it down?

    The question:

    Suppose you borrow P dollars at a monthly interest rate of r (as a decimal) and wish to pay off the loan in t months. Then your monthly payment can be calculated using the following formula in dollars.

    M = \frac {Pr(1+r)^t}{(1+r)^t-1}

    Remember that for monthly compounding, you get the monthly rate by dividing the APR by 12. Suppose you borrow $9000 at 9% APR (meaning that you use r = 0.09/12 in the preceding formula) and pay it back in 2 years.

    (With this information, I deducted:
    M = \frac {9000*0.0075(1+0.0075)^t}{(1+0.0075)^t-1}
    is that correct?)


    (a) What is your monthly payment? (Round your answer to the nearest cent.)

    (Is this t(1)?)

    (b) Lets look ahead to the time when the loan is paid off. (Round your answers to the nearest cent.)

    (i) What is the total amount you paid to the bank?

    (ii) How much of that was interest?

    (What does that mean...?)

    (c) The amount B that you still owe the bank after making k monthly payments can be calculated using the variables r, P, and t. The relationship is given by the formula below in dollars.

    B = P \left( \frac {(1+r)^t-(1+r)^k}{(1+r)^t-1}\right)

    (What... wait. Where did k come from? It says that k is the monthly payments... er. What? Two variables?)


    (i) How much do you still owe the bank after 1 year of payments? (Round your answer to the nearest cent.)

    (...Is that when t or k equals 12?)
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  2. #2
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    Quote Originally Posted by MathBane View Post
    Remember that for monthly compounding, you get the monthly rate by dividing the APR by 12. Suppose you borrow $9000 at 9% APR (meaning that you use r = 0.09/12 in the preceding formula) and pay it back in 2 years.
    (With this information, I deducted:
    M = \frac {9000*0.0075(1+0.0075)^t}{(1+0.0075)^t-1}
    is that correct?)

    ANSWER: Yes, correct; t = 24 (2 years = 24 months)

    (a) What is your monthly payment? (Round your answer to the nearest cent.)
    (Is this t(1)?)

    ANSWER: That question makes no sense...
    Do the calculation above (with t=24) and you'll get the monthly payment.
    .
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  3. #3
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    (a) What is your monthly payment? (Round your answer to the nearest cent.)

    411.16


    Thanks for your reply, but I am still having a lot of trouble with the rest of the problem.


    (b) Lets look ahead to the time when the loan is paid off. (Round your answers to the nearest cent.)

    (i) What is the total amount you paid to the bank?

    (ii) How much of that was interest?


    Wait, what does that stuff even mean? Do I have to add up all the numbers in the table to get the total? Do I minus the extra money from 9000 to get interest?


    B = P \left( \frac {(1+r)^t-(1+r)^k}{(1+r)^t-1}\right)

    I try to chuck that bad boy into the calculator and I enter parenthesis hell. No matter how hard I try, I get weird answers in the negatives. I assume k = 411.16... so...

    9000(((1+0.0075)^t-(1+0.0075)^411.16)/((1+0.0075)^t-1))

    That's how I've been putting it into the calculator. My syntax must be wrong to the extream.
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  4. #4
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    Quote Originally Posted by MathBane View Post
    (a) What is your monthly payment? (Round your answer to the nearest cent.)
    411.16
    (b) Lets look ahead to the time when the loan is paid off. (Round your answers to the nearest cent.)
    (i) What is the total amount you paid to the bank?
    (ii) How much of that was interest?
    411.16 is correct.

    Part (b) is really easy...you are complicating it.
    You paid back 411.16 * 24 = 9867.84.
    You obtained $9000 from the loan; so interest is 9867.84 - 9000 = 867.84.

    Total payments minus amount borrowed = interest cost.
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