Question

You want to buy a new sports car for $55,000. The contract is in the form of a 60 -month ordinary annuity at a 6 percent interest rate, compounded monthly. What will your monthly pavment be?

Answer 1

To calculate the monthly payment of a car loan, use the formula for the present value of an ordinary annuity. Substituting the given values into the formula, the monthly payment for a $55,000 sports car with a 6% interest rate compounded monthly over a 60-month period is approximately $1049.14.

Step-by-step explanation:

Mathematics: Calculating the Monthly Payment of a Car Loan

To calculate the monthly payment of the car loan, we can use the formula for the present value of an ordinary annuity:

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

Where:
PV is the present value (purchase price of the car),
PMT is the monthly payment,
r is the annual interest rate (6% or 0.06 as a decimal),
n is the number of compounding periods per year (12 for monthly compounding),
t is the total number of years (5 for a 60-month loan).

Substituting the given values into the formula, we get:

55000 = PMT * ((1 - (1 + 0.06/12)^(-12*5)) / (0.06/12))

Simplifying and solving for PMT:

PMT = 55000 / ((1 - (1 + 0.06/12)^(-12*5)) / (0.06/12))

Using a calculator or spreadsheet software, we find that the monthly payment is approximately $1049.14.

Answer 2

To calculate the monthly payment for a loan in the form of an ordinary annuity, you can use the formula :

PMT = P × (i(1+i)^n)/((1+i)^n - 1).

By plugging in the values, the monthly payment for the sports car would be approximately $1,063.05.

To calculate the monthly payment for a loan in the form of an ordinary annuity, we can use the formula :

PMT = P × (i(1+i)^n)/((1+i)^n - 1)

Where,

• PMT is the monthly payment
• P is the principal loan amount (price of the car)
• i is the interest rate per period (6% divided by 12 months)
• n is the total number of periods (60 months)

Plugging in the values :

PMT = 55000 × (0.06/12 × (1+0.06/12)^60)/((1+0.06/12)^60 - 1)

After evaluating the expression, the monthly payment for the sports car would be approximately $1,063.05.