Final answer:
John Fare's semiannual payment is $1,886.19 for the equipment purchase. Over 3 years, the total amount paid is $13,317.14, which includes a total interest of $3,317.14.
Step-by-step explanation:
John Fare purchased $12,000 worth of equipment making a $2,000 down payment and financing the rest at 8% interest compounded semiannually over 3 years. The formula for the semiannual payment when dealing with an annuity is P = (r*PV) / [1 - (1 + r)^(-n)], where P is the periodic payment, r is the interest rate per period, PV is the present value of the loan, and n is the number of periods.
To calculate the size of each semiannual payment (a), we must first determine r (the semiannual interest rate) and n (the total number of semiannual periods). r is 4% (0.08/2) and n is 6 (3 years * 2 periods per year). The present value PV that will be financed is $10,000 ($12,000 - $2,000 down payment). The payment P is calculated as follows: P = (0.04*$10,000) / (1 - (1 + 0.04)^(-6)) = $1,886.19 per payment, to two decimal places.
The total amount paid over the life of the loan (b) includes the down payment and all semiannual payments. Therefore, total amount paid = down payment + (payment P * n), which is $2,000 + ($1,886.19 * 6) = $13,317.14.
To find the total interest paid (c), we subtract the original loan amount from the total amount paid. Total interest = total amount paid - original loan amount. So, total interest = $13,317.14 - $10,000 = $3,317.14 total interest paid.