Rancher Rick purchased an additional 80 acres of hay ground to produce hay for his Angus herd. He paid $700/acre. He paid $20,000 down and took out a 10 year loan with interest calculated using add-on interest for the rest of the cost of the land. Assume annual payments and 5% interest rate. What is the amount of total interest paid over the lif of the loan?
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To find the total interest paid over the life of the loan, we need to calculate the annual payment and then subtract the principal amount.
First, let's calculate the principal amount of the loan. Rancher Rick purchased 80 acres of hay ground at $700 per acre, so the cost of the land would be 80 acres * $700 per acre = $56,000.
He made a down payment of $20,000, so the loan amount would be $56,000 (cost of land) - $20,000 (down payment) = $36,000.
Now, let's calculate the annual payment. Rancher Rick took out a 10-year loan with a 5% interest rate. To calculate the add-on interest, we need to add the interest to the principal amount and then divide it by the number of years.
Interest = Principal amount * Interest rate = $36,000 * 5% = $1,800
Total Amount = Principal amount + Interest = $36,000 + $1,800 = $37,800
Annual payment = Total Amount / Number of years = $37,800 / 10 = $3,780
Now that we know the annual payment, let's find the total interest paid over the life of the loan.
Total interest paid = (Annual payment * Number of years) - Principal amount = ($3,780 * 10) - $36,000 = $37,800 - $36,000 = $1,800
Therefore, the amount of total interest paid over the life of the loan is $1,800.