Question

You want to buy a new sports car from Muscle Motors for $76,000. The contract is in the form of a 60-month annuity due at an APR of 7.15 percent. What will your monthly payment be?

Answer 1

The monthly payment for the sports car will be approximately $1,507.68.

Step-by-step explanation:

To calculate the monthly payment on a 60-month annuity due, we can use the formula for the present value of an annuity due:

PV = PMT × [1 - (1 + r/n)^(-nt)] / (r/n)

Where:

• PMT = Monthly payment
• r = Annual interest rate
• n = Number of compounding periods per year
• t = Number of years

Plugging in the given values, we have:

76000 = PMT × [1 - (1 + 0.0715/12)^(-60)] / (0.0715/12)

Simplifying the equation, we find that the monthly payment (PMT) is approximately $1,507.68.

Answer 2

The formula of the future value of an annuity due is
Fv=pmt [(1+r/k)^(n)-1)÷(r/k)]×(1+r/k)
Fv future value 76000
PMT monthly payment?
R interest rate 0.0715
K compounded monthly 12
N time 60 months
Solve the formula for PMT
PMT=Fv÷[(1+r/k)^(n)-1)÷(r/k)]×(1+r/k)
PMT=76,000÷((((1+0.0715
÷12)^(60)−1)÷(0.0715÷12))
×(1+0.0715÷12))
=1,051.18 ....answer

Hope it helps!