Question

Phil can afford $200 a month for 5 years for a car loan. if the interest rate is 7.5 percent, how much can he afford to borrow to purchase a car?

Answer 1

200 per month for 5 years = 12,000
Phil can (at most) pay 12,000 for the car loan.
That would be the payment total.
So, how do we solve for the PRINCIPAL?
Looking at the attached formula, we see the
principal = Total - Total * ((1 +r)^-n) / r * n
where n = # of payments = 5 year * 12 months = 60 and
rate / 1.200 = 7.5/1,200 = .00625
 
principal = [12,000 - 12,000 * (1.00625)^-60] / .375
principal = [12,000 - 12,000 * 0.6880918239 ] / .375
principal = [12,000 - 8,257.1018863488] / .375
principal = 3,742.90 / .375
principal = 9,981.06

Source:
http://www.1728.org/loanfrm4.htm

Answer 2

Answer:

$24,952.65

Step-by-step explanation:

Phil can afford $200 a month for 5 years for a car loan. if the interest rate is 7.5 percent.

Loan formula:

$E=\dfrac{P\cdot \frac{r}{n}}{1-(1+\frac{r}{n})^{-n\time t}}$

where,

P is loan amount, P=?

E is monthly payment, E=$500

n is payment mode, n=12

t is time, t=5 years

r is rate of interest, r = 0.075

Substitute the value into formula and solve for P

$500=\dfrac{P\cdot \frac{0.075}{12}}{1-(1+\frac{0.075}{12})^{-12\time 5}}$

$P=\frac{500\cdot\left(1-\left(1+\frac{0.075}{12}\right)^{-60}\right)}{\frac{0.075}{12}}$

$P=24952.65$

Hence, Phil can borrow to purchase a car be $24,952.65