A sailboat costs $20019 . You pay 15% down and amortize the rest with equal monthly payments over a 12 -year period. If you must pay 7.8% compounded monthly, what is your monthly payment? How much interest will you pay?
First, calculate the down payment: $20019 * 15% = $<<20019*15*.01=3002.85>>3002.85
Then subtract the down payment from the total cost to find the amount of the loan: $20019 - $3002.85 = $<<20019-3002.85=17016.15>>17016.15
Next, calculate the number of monthly payments over 12 years: 12 years * 12 months/year = <<12*12=144>>144 months
Then calculate the interest rate per month: 7.8% / 100 / 12 = <<7.8/100/12=0.0065>>0.0065
Now use the formula for calculating the monthly payment on a loan:
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount
r = Monthly interest rate
n = Total number of monthly payments
M = $17016.15 * 0.0065 * (1 + 0.0065)^144 / ((1 + 0.0065)^144 - 1) = $<<17016.15*0.0065*(1+0.0065)^144/((1+0.0065)^144-1)=188.61>>188.61
The monthly payment is $188.61.
Now calculate the total interest paid over the term of the loan: $188.61 * 144 months - $17016.15 = $<<188.61*144-17016.15=1530.39>>1530.39
So, the total interest paid is $1530.39.