A sailboat costs $19,590. You pay 25% down and amortize the rest with equal monthly payments over a 8-year period. If you must pay 6.9% compounded monthly, what is your monthly payment? How much interest will you pay? ***
The initial down payment is 25% of the total price: \n\n25/100 * $19,590 = $4,897.50\n\nThe remaining balance to be financed is: \n\n$19,590 - $4,897.50 = $14,692.50.\n\nSince the loan is compounded monthly with an annual interest rate of 6.9%, we can calculate the monthly interest rate by dividing 6.9%/12, and the total number of payments as \n\n8 years*12 = 96 months.\n\nThe formula for the monthly payment of a loan is P[r(1 + r)^n] / [(1 + r)^n – 1]. Here, P is the principal amount, r is the monthly interest rate, and n is the number of payments. \n\nSo, the monthly payment = $14,692.50 * [0.00575(1 + 0.00575)^96] / [(1 + 0.00575)^96 – 1]\n\nCalculate the value in the bracket first.\n\nMonthly payment = $14,692.50 * 0.014965955146379067 ≈ $219.98.\n\nThe total amount paid overtime will be monthly payment * number of payments,\n\nTotal paid = $219.98 * 96 ≈ $21,118.08.\n\nTotal Interest paid is the Total amount paid less the principal amount,\n\nInterest Paid = $21,118.08 - $14,692.50 = $6,425.58.