# 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.

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}