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A sailboat costs $22,422. You pay 10% down and amortize the rest

with equal monthly payments over a 11​-year period. If you must pay
6.9% compounded​ monthly, what is your monthly​ payment? How

1 Answer

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Final answer:

The monthly payment for the sailboat can be calculated using the amortizing loan payment formula with a principal of $20,179.80, a monthly interest rate of 0.00575, and a total of 132 payments over 11 years.

Step-by-step explanation:

To calculate the monthly payment for a sailboat with the given parameters, we use the formula for the monthly payment on an amortizing loan, which is:

M = P * (i(1+i)^n) / ((1+i)^n - 1)

Where M is the monthly payment, P is the principal loan amount after down payment, i is the monthly interest rate, and n is the total number of payments.

The boat costs $22,422, and a 10% down payment would be 0.10 * $22,422 = $2,242.20. The amount to be amortized is $22,422 - $2,242.20 = $20,179.80

The monthly interest rate is 6.9% annually, which when divided by 12 equals 0.575% per month, or in decimal form, 0.00575.

The total number of monthly payments over 11 years is 11 * 12 = 132.

Plugging these values into the formula:

M = $20,179.80 * (0.00575(1+0.00575)^132) / ((1+0.00575)^132 - 1)

When you do the calculations, you'll find the monthly payment amount that will be required.

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