# Math Help - Car Buying-Compound interest

1. ## 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. 2. 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.

3. 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. 4. Originally Posted by seeke -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....

5. Originally Posted by seeke
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)