Answer:
Explanation:
To find the size of the monthly payments, we can use the formula for the present value of an annuity.
1. Identify the given information:
- Immediate payment option: $19,700
- Payment period: 8 years
- Interest rate: 10.43% compounded monthly
2. Calculate the monthly interest rate:
- Monthly interest rate = Annual interest rate / Number of compounding periods per year
- Monthly interest rate = 10.43% / 12 = 0.8692% (rounded to four decimal places)
3. Calculate the number of monthly payments:
- Number of monthly payments = Payment period * Number of compounding periods per year
- Number of monthly payments = 8 years * 12 = 96
4. Calculate the size of the monthly payments using the present value of an annuity formula:
- Monthly payment = Present value / [(1 - (1 + interest_rate)^(-number_of_payments)) / interest_rate]
- Monthly payment = $19,700 / [(1 - (1 + 0.008692)^(-96)) / 0.008692]
- Monthly payment = $19,700 / (0.008692 / (1 - 1.008692^(-96)))
- Monthly payment = $19,700 / (0.008692 / (1 - 0.158611))
- Monthly payment = $19,700 / (0.008692 / 0.841389)
- Monthly payment = $19,700 / 0.010336
- Monthly payment ≈ $1,905.03 (rounded to the nearest cent)
Therefore, the size of the monthly payments, at an interest rate of 10.43% compounded monthly, would be approximately $1,905.03.