MAT $1010$

Loan Repayment $($see also Ch $19\mathrm{.}1)$

September $5,2023$

$2.$ We might want to figure out how much time it would take to pay back a loan at a certain rate and regularly scheduled payment. In order to do that, we'd need to solve for $n$ in the loan repayment formula above. This sort of problem is one place logarithms can help! Consider the following example: Suppose Angelica buys a $$23,000$ car. She puts $10\%$ down and finances the rest at $12\mathrm{.}4\%$

$($a$)$ According to her original plan to pay off the loan in $4$ years, what would her monthly payments be $($this part uses the loan formula as before$)?$

$($b$)$ Suppose Angelica decides to pay $$800$ per month instead. How many months $n$ will it take to pay off her loan?