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 calculate the monthly payment, we need to determine the loan amount after the down payment.
10% of $20842 is (10/100) * $20842 = $2084.2
The loan amount is $20842 - $2084.2 = $18757.8
To determine the monthly payment, we can use the formula for the monthly payment on an amortizing loan:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = monthly payment
r = monthly interest rate
PV = loan amount
n = number of months
The monthly interest rate is (6.6/100) / 12 = 0.0055
The loan amount is $18757.8
The number of months is 14 * 12 = 168
P = (0.0055 * $18757.8) / (1 - (1 + 0.0055)^(-168))
Using a calculator, we find that P ≈ $168.66
Therefore, your monthly payment will be approximately $168.66.
To determine the total interest paid over the 14-year period, we can subtract the loan amount from the total amount paid.
Total amount paid = $20842 (initial cost of the sailboat) + ($168.66/month * 168 months)
Total amount paid = $20842 + (168.66 * 168)
Total amount paid = $20842 + $28360.88
Total amount paid = $49202.88
Interest paid = Total amount paid - Loan amount
Interest paid = $49202.88 - $18757.8
Interest paid = $30445.08
Therefore, you will pay approximately $30445.08 in interest over the 14-year period.
To find the monthly payment and the amount of interest paid, we can use the formula for calculating the monthly payment on a loan:
A = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
A = monthly payment
P = principal loan amount
r = monthly interest rate
n = total number of payments
First, let's calculate the values needed for the formula:
Principal loan amount (P) = $20,842 - (10% of $20,842)
P = $20,842 - ($20,842 * 0.10)
P = $20,842 - $2,084.20
P = $18,757.80
Monthly interest rate (r) = 6.6% / 100% / 12 months
r = 0.066 / 12
r = 0.0055
Total number of payments (n) = 14 years * 12 months per year
n = 14 * 12
n = 168
Now, let's plug the values into the formula:
A = $18,757.80 * (0.0055 * (1 + 0.0055)^168) / ((1 + 0.0055)^168 - 1)
Using a calculator, the monthly payment (A) is approximately $176.24.
To calculate the total interest paid, we can multiply the monthly payment by the total number of payments and subtract the principal loan amount:
Total interest paid = ($176.24 * 168) - $18,757.80
Total interest paid = $29,631.12 - $18,757.80
Total interest paid = $10,873.32
Therefore, the monthly payment is approximately $176.24, and the total interest paid is $10,873.32.
To find the monthly payment, we need to use the formula for the monthly payment of an amortized loan:
A = P * (r * (1+r)^n) / ((1+r)^n - 1)
where:
A = monthly payment
P = principal loan amount
r = monthly interest rate
n = total number of monthly payments
First, let's calculate the principal loan amount by subtracting the down payment from the sailboat cost:
Principal loan amount = Sailboat cost - (10% of Sailboat cost)
Principal loan amount = $20,842 - (0.1 * $20,842) = $18,757.80
Next, let's calculate the monthly interest rate by dividing the annual interest rate by 12 and converting it to decimal:
Monthly interest rate = (Annual interest rate / 12) / 100
Monthly interest rate = (6.6 / 12) / 100 = 0.0055
Now, let's calculate the total number of monthly payments by multiplying the number of years by 12:
Total number of monthly payments = 14 years * 12 months/year
Total number of monthly payments = 168
Plug these values into the formula:
A = $18,757.80 * (0.0055 * (1+0.0055)^168) / ((1+0.0055)^168 - 1)
Now, let's calculate the monthly payment:
A = $18,757.80 * (0.0055 * (1+0.0055)^168) / ((1+0.0055)^168 - 1)
A ≈ $160.64
Therefore, your monthly payment for the sailboat is approximately $160.64.
To calculate the total interest paid over the 14-year period, you can multiply the monthly payment by the total number of payments and subtract the principal loan amount:
Total interest paid = (A * n) - P
Total interest paid = ($160.64 * 168) - $18,757.80
Total interest paid ≈ $7,418.72
Therefore, you will pay approximately $7,418.72 in interest over the 14-year period.