Question

Mr. Brown wants to buy a Tesla Model S car, whose price is $100, 848. The dealer offers a loan plan: $30, 000 downpayment, $X at the end of year 1, year 2, year 3, and year 4. Assume the constant annual interest rate is 25%. (a) What is X

Answer 1

X is $30,000

Step-by-step explanation:

First, we need to calculate the Amount ofLoan

Amount of Loan = Car price - Down payment = $100,848 - $30,000 = $70,848

This is the situation of annuity payment for 4 years at a 25% interest rate with equal annuity payment each year.

Now we will use the following formula to calculate the value of X

PV of Annuity = Annuity payment x ( 1 - ( 1 + interest rate )^-numbers of years ) / Interest rate

Where

PV of Annuity = Amount of Loan = $70,848

Interest rate = 25%

Numbers of years = 4 years

Annuity Payment = X = ?

Placing values in the formula

$70,848 = X x ( 1 - ( 1 + 25% )^-4 ) / 25%

$70,848 = X x 2.3616

X = $70,848 / 2.3616

X = $30,000