Suppose you borrowed $15000 to buy a car at an interest rate 7.2% compounded monthly. What will the monthly payments be on loans of 36, 48 and 60 months if you do not have to put any money down on the financing?

There is an ambiguity in the question to be clarified about the interest rate.

Generally annual interest is quoted. The wording of the question casts a doubt as to 7.2% is monthly or annual interest.

Considering that 86.4% annual interest is illegal in some countries, 7.2% will be considered annual interest.

The monthly payment can be calculated by equating future values and simplification using factorization:
P(1+r)^n = M(1+r+r^2+...+r^(n-1))
=M((1+r)^n-1)/((1+r)-1)
=M((1+r)^n-1)/r
P=present value
M=monthly payment
r=interest per period (month)
n=number of periods (month)
Solve for M:
M=Pr(1+r)^n/((1+r)^n-1)

substituting n=36, r=7.2%/12=0.006,P=15000,
M=15000*0.006*(1.006^36)/(1.006^36-1)
=464.53

Rough check:
For short terms (under 10 years) the total amount paid should cost a little more than the simple interest paid over half the period.
15000*(1+3(years)/2*0.072)=16620
464.53*36=16723 slightly >16620
so ok.

I will leave it to you to tackle the other periods. Post your answer for checking if you wish.

To calculate the monthly payments on a loan, you can use the formula for the monthly payment on an installment loan:

P = (r * PV) / (1 - (1 + r)^(-n))

Here:
P = Monthly Payment
r = Monthly interest rate (annual interest rate divided by 12)
PV = Present value (Loan amount)
n = Number of months

First, we need to calculate the monthly interest rate. The annual interest rate is 7.2%, so the monthly interest rate is 7.2% / 12 = 0.72% or 0.0072.

Now, let's calculate the monthly payments for each loan term:

For a 36-month loan:
PV = $15,000
r = 0.0072
n = 36

P = (0.0072 * $15,000) / (1 - (1 + 0.0072)^(-36))
P = $470.68 (rounded to the nearest cent)

The monthly payments for the 36-month loan would be approximately $470.68.

For a 48-month loan:
PV = $15,000
r = 0.0072
n = 48

P = (0.0072 * $15,000) / (1 - (1 + 0.0072)^(-48))
P = $365.88 (rounded to the nearest cent)

The monthly payments for the 48-month loan would be approximately $365.88.

For a 60-month loan:
PV = $15,000
r = 0.0072
n = 60

P = (0.0072 * $15,000) / (1 - (1 + 0.0072)^(-60))
P = $304.99 (rounded to the nearest cent)

The monthly payments for the 60-month loan would be approximately $304.99.