Answer:
She should borrow the money for 3.1161... years so that she can afford the monthly payment.
Step-by-step explanation:
Monthly payment formula is: [tex]M=P*\frac{r(1+r)^n}{(1+r)^n -1}[/tex] , where
M = Monthly payment amount, P = Loan amount, r = rate of interest per month and n = total number of months.
Given that, Cynthia wants to take out a $8500 loan with a 4.75% APR and she can afford to pay $245 per month.
That means, [tex]P= 8500, M= 245[/tex] and [tex]r= \frac{0.0475}{12}= 0.0039583[/tex]
Plugging these values into the above formula, we will get........
[tex]245=8500*\frac{0.0039583(1+0.0039583)^n}{(1+0.0039583)^n-1} \\ \\ 245=\frac{33.64555(1.0039583)^n}{(1.0039583)^n -1}\\ \\ 245(1.0039583)^n -245=33.64555(1.0039583)^n\\ \\ 211.35445(1.0039583)^n=245\\ \\ (1.0039583)^n=\frac{245}{211.35445}=1.15919\\ \\ n= log_{1.0039583}(1.15919)=37.39327[/tex]
So, [tex]n= 37.39327 months =\frac{37.39327}{12} years = 3.1161... years[/tex]
That means, she should borrow the money for 3.1161... years so that she can afford the monthly payment.
