Question

Lexi wants to buy a Tesla Model S . The car will cost​ $68,000 and she has​ $20,000 as a down payment. If she will finance the rest with a 4 year​ 6% APR loan with monthly​ payments, how much will her monthly payments​ be?

Answer 1

`\large \boxed{\$1127.28}`

Step-by-step explanation:

For an amortized loan, paying back a fixed amount periodically, the formula for each payment is

a = P\left (\dfrac{r(1 + r)^{n}}{(1 +r)^{n} - 1}

where

a = payment amount per period

P = principal (loan amount)

r = interest rate per period

n = total number of periods (payments)

Data:

Cost = $68 000

Down payment = $20 000

Term of loan = 4 yr

APR = 6 %

Payments = monthly

Calculations:

P = $68 000 - $20 000 = $48 000

n = 4 × 12 = 48

r = 0.06/12 = 0.005

`\begin{array}{rcl}a&=& 48000\left ((0.005(1 +0.005)^(48))/((1 + 0.005)^(48) - 1) \right )\\\\&=& 48000\left ((0.005(1.005)^(48))/((1.005)^(48) - 1) \right )\\\\&=& 48000\left ((0.005 * 1.270489)/(1.2704892 - 1) \right )\\\\&=& 48000\left ((0.006352446)/(0.2704892) \right )\\\\& =& 480000* 0.02348503\\\& =& \mathbf{\$1127.28}\\\\\end{array}\\\text{Their monthly payments will be $\large \boxed{\mathbf{\$1127.28}}$}`