Final answer:
The remaining balance on the loan on Jan. 1, 2005 is $54,000.
Step-by-step explanation:
To find out how much is owed on the loan on Jan. 1, 2005, we need to determine the remaining balance after each payment.
On Jan. 1, 1996, $5,000 is paid, leaving a remaining balance of $40,000 - $5,000 = $35,000.
On Jan. 1, 1997, another $5,000 is paid, leaving a remaining balance of $35,000 - $5,000 = $30,000.
On Jan. 1, 1998, an additional $5,000 is paid, reducing the remaining balance to $30,000 - $5,000 = $25,000.
On July 1, 1998, an extra payment of $10,000 is made, further reducing the remaining balance to $25,000 - $10,000 = $15,000.
No more payments are made after this point. We need to calculate the interest on the remaining balance for the period from July 1, 1998 to Jan. 1, 2005.
The interest rate per period is given as d^(4) = 0.1. This means that the interest rate per year is 0.10 * 4 = 0.40 or 40%.
The period from July 1, 1998 to Jan. 1, 2005 is 6.5 years. Therefore, the interest on the remaining balance is $15,000 * 0.40 * 6.5 = $39,000.
The total amount owed on Jan. 1, 2005 is the remaining balance plus the interest, which is $15,000 + $39,000 = $54,000.