To find the unpaid balance after 13 months, we need to calculate how much of the loan principal has been paid off by the monthly payments. We can use an amortization table to help with this calculation.
Month Payment Interest Principal Balance
0 - - - 85,000.00
1 498.74 410.83 87.91 84,912.09
2 498.74 409.63 89.11 84,823.98
3 498.74 408.42 90.32 84,733.67
...
12 498.74 398.29 100.45 83,810.25
13 498.74 397.06 101.68 83,708.57
So after 13 months, the unpaid balance on the loan is $83,708.57.
To calculate how much interest the executive paid during this time period, we can subtract the amount of principal paid from the total amount of payments made and then round to two decimal places:
Total payments made in 13 months = $498.74/month x 13 months = $6,482.62
Interest paid = Total payments made - Principal paid = $6,482.62 - $1,307.50 = $5,175.12
Therefore, the executive paid $5,175.12 in interest during the first 13 months of the loan.