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

$18,089.96

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*((1+i)^n-1)/(i(1+i)^n)`

or

`\textup{Present value}=2016*((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