Question

You are looking to purchase a Tesla Model X sport utility vehicle. The price of the vehicle is $95,750. You negotiate a six-year loan, with no money down and no monthly payments during the first year. After the first year, you will pay $1,525 per month for the following five years, with a balloon payment at the end to cover the remaining principal on the loan. The APR on the loan with monthly compounding is 4.6 percent. What will be the amount of the balloon payment six years from now?

Answer 1

Solution

Total loan amount today= 95750

Loan tenure = 6 Years

APR= 4.6%

Monthly interest rate=.046/12= 0.003833

Now The Loan amount should be equal to Present Value(PV) of monthly installments+PV of the balloon payment

PV= Cashflow/(1+r)^n

Calculation of PV of monthly payments is given below

Excel formula

Now The Loan amount should be equal to Present Value(PV) of monthly installments+PV of the balloon payment

95750=77939.1146+PV of the balloon payment

PV of balloon payment= Baloon payment/(1+r/12)^n*12

Therefore

95750=77939.1146+Baloon payment/(1+r/12)^n*12

17810.88535=Baloon payment/(1+r/12)^n*12

17810.88535=Baloon payment/(1+.046/12)^6*12

Baloon payment=17810.88535*1.317152682

=23459.65541

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