Answer:
$255.01
Step-by-step explanation:
To find the monthly payment needed to pay off a loan of $6,500 in 3 years at 24% interest compounded monthly, we can use the Monthly Payment formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Monthly Payment Formula}}\\\\M=\dfrac{Pr\left(1+r\right)^{n}}{\left(1+r\right)^{n}-1}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$M$ is the monthly payment.}\\\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount (loan amount).}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate per month (in decimal form).}\\\phantom{ww}\bullet\;\;\textsf{$n$ is the term of the loan (in months).}\\\end{array}}[/tex]
In this case:
- P = $6,500
- r = 24%/12 = 0.24/12 = 0.02
- n = 3 years = 3 × 12 = 36 months
Substitute the values into the formula and solve for M:
[tex]M=\dfrac{6500\cdot 0.02(1+0.02)^{36}}{(1+0.02)^{36}-1}\\\\\\M=\dfrac{130(1.02)^{36}}{(1.02)^{36}-1}\\\\\\M=255.013541...\\\\\\M=\$255.01[/tex]
Therefore, the monthly payment rounded to the nearest cent is:
[tex]\Large\boxed{\boxed{\$255.01}}[/tex]
