Suppose the interest rate on the car loan is r% and equal monthly payments are to be made for t years. Then for each $1200 borrowed the monthly payment M is given by

$$M = \frac{r}{1 - (1 + \frac{r}{1200})^{-12t}}$$

If you buy a Mini-Cooper costing $24, 000 what will your monthly payment be on a 3 year loan when the interest rate on the loan is 6%?

To solve this problem, I first plugged in the $r$ and $t$ values into the equation, which gave me approximately $\$33.36$. However, all of the possible answers for this question are in the $\$700$ range, so I'm uncertain of how to proceed. I'm also uncertain of what the question is asking in the first place - for instance, why is $\$1200$ relevant to begin with? I tried doing $\frac{24000}{33.36}$, and that gave me $\$719.33$, which was not one of the answers either.

Can someone point me in the right direction here?


Your formula is messed up. First, the whole mess should be multiplied by the PV (present value) which is \$24,000. Second, there's a confusion in the $r$. The 1200 is not a dollar amount, but 12 times 100. The 12 is because the rate is in years, but the payment is in months. The 100 is to convert the $r=6$ into $6\%$. Which means that the $r$ in the numerator should be divided by 100 also. (Either $r=6$ and we talk about $r\%$ or $r=0.06$ and we talk about the rate being $r$ (no percent sign.) This formula is mixing the two ways to do it.) Also the numerator should be divided by 100 if the $r$ in the denominator is.)

That makes the calculation $0.0304$ times PV = \$730.13.$


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