Final answer:
Skyler owes approximately $8,444.33 in June 2022. Each monthly payment for amortizing the loan over 2 years starting in June 2022 would be approximately $374.67.
Step-by-step explanation:
To calculate how much Skyler owes in June 2022, we can use the compound interest formula: A = P * (1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, Skyler borrowed $8,000 with an interest rate of 11/2% per year compounded monthly. So, P = $8,000, r = 11/2% = 0.015, n = 12 (monthly compounding), and t = 2 years.
By substituting these values into the formula, we get:
A = $8,000 * (1 + 0.015/12)^(12 * 2)
After calculation, Skyler would owe approximately $8,444.33 in June 2022.
To calculate the size of each monthly payment for amortizing the loan over 2 years starting in June 2022, we can use the amortization formula: P = (r / (1 - (1 + r)^(-nt))) * A, where P is the monthly payment, r is the interest rate per period, n is the number of payments per year, t is the total number of years, and A is the loan amount.
In this case, Skyler owes $8,444.33, and he will make monthly payments for 2 years. So, A = $8,444.33, r = 0.015/12 (monthly interest rate), n = 12 (monthly payments), and t = 2 years.
By substituting these values into the formula, we get:
P = (0.015/12) / (1 - (1 + 0.015/12)^(-12 * 2)) * $8,444.33
After calculation, each monthly payment for Skyler would be approximately $374.67.