# Dean is planning to purchase a New Nissan Altima which costs $26,865. He saved$3,200 to put...

Dean is planning to purchase a New Nissan Altima which costs {eq}\$26,865 {/eq}. He saved {eq}\$3,200 {/eq} to put toward it. He is thinking about getting a loan for it from his credit union, but he could also keep driving his beat up old car for a while longer and save up cash for this one. Dean qualifies for a {eq}5 {/eq} year loan from his credit union with a {eq}6.4 \% {/eq} APR. If he uses the {eq}\$3,200 {/eq} as a down payment, what percent down payment will be making? ## Simple Interest: Simple interest is the simplest method of determining the interest that one accrues overtime on a principal amount, usually on a loan. It is the the additional amount you pay apart from the principal loan amount you repay over a period of time. Typically, simple interest rate is calculated on the annual basis and therefore referred to as annual percentage rate or APR. If {eq}P {/eq} is the principal amount, {eq}R {/eq} is the interest rate and {eq}T {/eq} is the time between two loan payments, then simple interest to be paid or {eq}I = P \times T \times R {/eq} ## Answer and Explanation: Initial cost to purchase a New Nissan Altima or {eq}P =$26, 865 {/eq}

The amount paid as a down payment or {eq}D = $3,2000 {/eq} The balance from the initial cost remaining after the down payment {eq}B = P- D =$26,865 - $3,200 =$23,665 {/eq}

The interest rate paid per year on balance for the next {eq}5 {/eq} years {eq}= 6.4 {/eq}%.

The amount of interest paid on the balance {eq}I = 5 \times 0.064 \times $23,665 =$7,572.8 {/eq}

Total amount to be paid at the end of five years or total cost of the vehicle including interest {eq}= P + I = $26,865 +$7,572.8 = \$34,437.8 {/eq}

The percent of total cost that down payment accounts for {eq}= \frac{3200}{34437.8} \times 100 = 9.29 {/eq}%

Dean will be making {eq}9.29 {/eq}% of the final cost of the vehicle as down payment. 