Final answer:
The principal reduction after the first year on a $150,000 loan at 6% with monthly payments of $850 cannot be given precisely without an amortization schedule, but a rough estimate can be calculated using the first month's principal reduction multiplied by 12, providing an approximate amount of $1,200 for the first year.
Step-by-step explanation:
Calculating the Principal Reduction After One Year
To calculate the principal reduction after the first year of a loan where the purchaser borrows $150,000 at 6% with a monthly payment of $850, one must understand how much of the monthly payment is going towards interest and how much is reducing the principal. Initially, the monthly interest can be calculated by multiplying the principal by the monthly interest rate (annual rate divided by 12). In this case, the first month's interest is $150,000 × (0.06/12) = $750. Subtracting this from the monthly payment gives us the principal reduction for the first month, which is $850 - $750 = $100.
However, for each subsequent month, the interest component of the payment will decrease slightly as the principal is reduced by the payments made, leading to a little more of the $850 payment going towards principal each month. Without an amortization schedule, it's not possible to give an exact figure for the reduction of the principal after one year, as this would require the calculation of each month's interest and principal repayment. However, for approximation, the first month's principal reduction can be multiplied by 12 to provide a rough estimate of the principal reduction for the year, which would be around $100 × 12 = $1,200 for the first year. This is an underestimate since it doesn't account for the compounding effect of monthly payments.
An exact answer would need the amortization schedule or use of a financial calculator or software designed for loan amortizations.