A sailboat costs 20842$ You pay 10% down and amortize the rest with equal monthly payments over a 14 -year period. If you must pay 6.6% compounded monthly.
what is your monthly payment?
How much interest will you pay?
To find the monthly payment, we need to calculate the principal amount that will be amortized and the interest rate per period.
Principal amount = Total cost - Down payment
Principal amount = $20842 - ($20842 * 0.10)
Principal amount = $20842 - $2084.20
Principal amount = $18757.80
Number of periods = 14 years * 12 months per year
Number of periods = 168 months
Monthly interest rate = (1 + interest rate)^periods - 1
Monthly interest rate = (1 + 0.066/12)^168 - 1
Monthly payment = Principal amount * Monthly interest rate / (1 - (1 + Monthly interest rate)^(-Number of periods))
Monthly payment = $18757.80 * [((1 + 0.066/12)^168 - 1) / (1 - (1 + 0.066/12)^(-168))]
Using the formula, the monthly payment is approximately $176.40.
To find the total interest paid, we can subtract the principal amount from the total amount paid over the 14-year period.
Total amount paid = Monthly payment * Number of periods
Total amount paid = $176.40 * 168
Total amount paid = $29635.20
Interest paid = Total amount paid - Principal amount
Interest paid = $29635.20 - $18757.80
The interest paid is approximately $10877.40.
To calculate the monthly payment, we can use the formula for the amortization of a loan:
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
M is the monthly payment,
P is the principal amount (cost of the sailboat - down payment),
r is the monthly interest rate (6.6% / 12 = 0.0055),
n is the total number of payments (14 years * 12 months = 168).
First, let's calculate the principal amount (P):
P = $20,842 - 10% down payment
P = $20,842 - ($20,842 * 0.1)
P = $20,842 - $2,084.2
P = $18,757.8
Next, let's calculate the monthly payment (M):
M = $18,757.8 * 0.0055 * (1 + 0.0055)^168 / ((1 + 0.0055)^168 - 1)
Using a calculator, the monthly payment comes out to be approximately $171.87.
To calculate the total interest paid, we can use the formula:
Total Interest = (M * n) - P
Where:
M is the monthly payment,
n is the total number of payments (168),
P is the principal amount ($18,757.8).
Total Interest = ($171.87 * 168) - $18,757.8
Using a calculator, the total interest paid comes out to be approximately $4,846.40
To find the monthly payment and the total interest paid, we can use the formula for amortized loans. The formula is:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ (-Number of Months))
To calculate the monthly payment, we need to find the Loan Amount, Monthly Interest Rate, and Number of Months.
1. Loan Amount: You pay 10% down on the sailboat, which means you need to find 90% of its cost. So, the Loan Amount is 90% of $20,842.
Loan Amount = $20,842 x 0.90 = $18,757.80
2. Monthly Interest Rate: The annual interest rate is 6.6%, compounded monthly. To find the monthly interest rate, we need to divide the annual interest rate by 12 (number of months in a year).
Monthly Interest Rate = 6.6% / 12 = 0.066 / 12 = 0.0055
3. Number of Months: The loan is amortized over a 14-year period. To find the number of months, we multiply the number of years by 12 (number of months in a year).
Number of Months = 14 x 12 = 168
Now, substitute the values into the formula:
Monthly Payment = ($18,757.80 * 0.0055) / (1 - (1 + 0.0055) ^ (-168))
Monthly Payment ≈ $165.32
So, the monthly payment for this loan would be approximately $165.32.
To find the total interest paid, we subtract the Loan Amount from the sum of all the monthly payments over the 14-year period.
Total Interest Paid = (Monthly Payment * Number of Months) - Loan Amount
Total Interest Paid = ($165.32 * 168) - $18,757.80
Total Interest Paid ≈ $9,210.86
Therefore, the total interest paid would be approximately $9,210.86.