Question

monthly payment 101
name savannah date 10/9
while spending only $2,000 to take home a brand new toyota camry may sound like a lot of fun, paying on that loan for 72 months may not be. in the united states, the commentary after our last economic collapse was that americans tend to buy things out of their reach. homes, cars, televisions, you name it, we buy it. perhaps shortsighted buyers expect a promotion that never comes or are on the receiving end of an unforeseen accident or illness. nonetheless understanding budgets and monthly payments is an essential component of an individuals financial literacy.
in this assignment, you will use a slightly intimidating looking equation: $p=\frac{cr(1 + r)^{n}}{(1 + r)^{n}-1}$ where...
$p =$ monthly payment, $c =$ loan amount, $n=$ the number of months and $r =$ monthly interest rate (a 7.5% annual rate would be converted to a decimal and divided by 12: 0.075/12 so 0.00625)
you will need to plug values into the formula and use the order of operations to calculate the monthly payments for the situations below. youll also determine the total amount of money the individual ends up spending on monthly payments. the difference between this amount and the original price tag is the interest on the loan. help these individuals figure out if the monthly payment fits in their budget and is worth it to them in the long run.
jessica is considering borrowing $15,000 for a new ford fusion if...
the monthly payment is less than $250 and the total cost is less than $16,000
equation space:
huffington bank loan offer
loan amount c $15,000
annual interest rate 6.0%
monthly interest rate (r) 0.005
number of months (n) 72
monthly payments (p) will be... $

1. based on your calculations, does the monthly payment fit into jessicas budget?
2. how much interest is jessica going to owe? will it put her over her goal of $16,000?
3. would you recommend this loan for her? why or why not?

long term cost
number of months n
monthly payments p
total cost np
interest np - c

Explanation:

Step1: Calculate monthly payment

We are given the formula $P=\frac{Cr(1 + r)^N}{(1 + r)^N-1}$, where $C = 15000$, $r=0.005$, and $N = 72$.
First, calculate $(1 + r)^N=(1 + 0.005)^{72}$.
Using the formula for compound - interest, $(1 + 0.005)^{72}\approx1.432044$.
Then, $Cr(1 + r)^N=15000\times0.005\times1.432044 = 107.4033$.
And $(1 + r)^N-1=1.432044 - 1=0.432044$.
So, $P=\frac{107.4033}{0.432044}\approx248.6$.

Step2: Calculate total cost

The total cost is $nP$, where $n = 72$ and $P\approx248.6$. So, $nP=72\times248.6 = 17899.2$.

Step3: Calculate interest

The interest is $nP - c$, where $nP = 17899.2$ and $c = 15000$. So, the interest is $17899.2-15000 = 2899.2$.

Answer:

1. Yes, the monthly payment of approximately $\$248.6$ is less than $\$250$, so it fits into Jessica's budget.
2. Jessica will owe an interest of $\$2899.2$. The total cost of $\$17899.2$ is more than her goal of $\$16000$.
3. No, I would not recommend this loan for her because the total cost of the loan exceeds her goal of $\$16000$, even though the monthly payment fits her monthly budget.