Question

You purchase a car worth $25077 and make a down payment of $3560. You intend to repay the balance of the car with month end car payments of $336 for 5 years and a final "buyout" at the end of 5 years. Money can earn 4.04% compounded semi-annually, What is the value of your car loan repayments in terms of dollars in 5 years? Answer:

Answer 1

Answer:

$18,089.96

Step-by-step explanation:

Given:

Worth of car = $25077

down payment = $3560

month end car payments = $336

Time period = 5 years

Interest rate, i = 4.04% compounded semi-annually

since, the interest is compounded semi-annually thus, the actual time period, n will be 5 × 2 = 10 fro semi annually

Total payment made semi annually, A = $336 × 6 = $2016

Now,

$\textup{Present value}=A\times\frac{(1+i)^n-1}{i(1+i)^n}$

or

$\textup{Present value}=2016\times\frac{(1+0.0404)^{10}-1}{0.0404(1+0.0404)^{10}}$

or

$\textup{Present value}=\ 18,089.96$

Thus,

The value of car loan payment is $18,089.96