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Math Help - Car Buying-Compound interest

  1. #1
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    Car Buying-Compound interest

    I'm checking answer for my sister. But since I no longer have the background in how to appropriately use the financial formulas, I post it here for help.

    Problem: A car that costs $10,000. I want to buy this car.
    -I have $2,500 to deposit right now toward a down payment. I can get a 6.5% interest rate if I deposit this $2,500 into a CD. This is a one time deposit of $2,500 compounded monthly and it is locked in for 2 years.
    -When I purchase this car in 2 years, I want to make $100 monthly payments for 3 years, and I project this loan will be at 4.2% interest.
    Question: What do I need to deposit monthly into an annuity for the next 24 months to obtain the rest of the down payment? I can earn 5% interest compounded monthly with this annuity.

    My first attempt I got $149.97, but my sister's answer is different ($145.85).

    I got confused after the $100 monthly payments part; and switched between different equations for PV and FV, thus different answers. There's a play of words here and it confuses me. I don't know if the rest of the down payment after 2-year-CD will have the 4.2% interest or the $10,000.
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  2. #2
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    Here is my other attempt at this:

    - After the CD, I have $2846.07
    So when I purchase the car, I have $10,000-$2846.07 = $7,153.93 left to pay off.

    -According to the wording of the problem, I assume I will be depositing $100 monthly for 3 years.
    So for 3 years I will make the total payment of: $100 x 12 months x 3 years = $3,600

    -But the (assumed annual) year interest for the $7,153.93 is at 4.2%
    So after 3 years it will be: $7153.93(1.042)^3= $8093.71
    Subtract it from the total payment, I have $8093.71 - 3600 = $4493.71 left to pay off.

    -So now how much I need to deposit monthly into an annuity for the next 24 months to obtain the $4493.73? I can earn 5% interest compounded monthly with this annuity.
    -I'm not sure what it means by "I can earn 5% interest compounded monthly with the annuity"

    -Hit the wall.
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  3. #3
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    Okay, seem like I incorrectly assume the $3,600 after 3 years as payment toward the $7,153.93
    -So I make a monthly payment of $100 for 3 years to pay off the $7,153.93. And this amount also have a 4.2% interest rate.
    -After much research, the amount left after 3 years of interest and my monthly payment of $100 is called the balloon payment. I need an equation to relate the rate, PMT, and FV.
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  4. #4
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    Quote Originally Posted by seeke View Post
    -So now how much I need to deposit monthly into an annuity for the next 24 months to obtain the $4493.73? I can earn 5% interest compounded monthly with this annuity.
    -I'm not sure what it means by "I can earn 5% interest compounded monthly with the annuity"
    Means you're paid .05/12 monthly.
    Monthly deposit required is 178.4223...

    Formula: F * i / [(1 + i)^n - 1]
    d = monthly deposit (?)
    F = future value (4493.73)
    i = interest (.05/12)
    n = number of deposits (24)

    d = 4493.73 * .05/12 / [(1 + .05/12)^24 - 1] = 178.4223....
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  5. #5
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    Quote Originally Posted by seeke View Post
    Okay, seem like I incorrectly assume the $3,600 after 3 years as payment toward the $7,153.93
    -So I make a monthly payment of $100 for 3 years to pay off the $7,153.93. And this amount also have a 4.2% interest rate.
    -After much research, the amount left after 3 years of interest and my monthly payment of $100 is called the balloon payment. I need an equation to relate the rate, PMT, and FV.
    IF YOU GOT THAT RIGHT (!) then balloon payment will be 4283.28.
    That's from (the FV of $7153.93) minus (the FV of 36 monthly payments of $100)
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