# A sailboat costs $28,867. You pay 2-% down payment and amortize the rest with eqaul monthly... ## Question: A sailboat costs$28,867. You pay 20% down payment and amortize the rest with eqaul monthly payment over a 9-yr period. If you must pay 6.9% compound monthly,

What is your monthly payment? (round to two decimal places)

How much interest will you pay? (round to two decimal places)

## Down Payment:

For large purchases such a house or a car, it is common to finance the purchase without loans. The down payment is the amount that paid upfront, while the remaining portion of cost is repaid through periodic payments.

## Answer and Explanation:

The monthly payment is \$287.65.

We can use the following formula to compute the monthly payment for a loan with principal {eq}P {/eq}, monthly interest rate {eq}r{/eq} and number of monthly payments {eq}T{/eq}:

• {eq}\displaystyle \frac{Pr}{1 - (1 + r)^{-T}} {/eq}

In this question, the amount borrowed is the cost minus the down payment, i.e.,

• 28,867 - 28,867 * 20% = 23,093.6

The monthly interest rate is 6.9% / 12 = 0.575%, and there are 9 * 12 = 108 monthly payments. Applying the formula, the monthly payment is:

• {eq}\displaystyle \frac{23,093.6*0.575\%}{1 - (1 + 0.575\%)^{-108}} = 287.65 {/eq}