Question

A contract can be fulfilled by making an immediate payment of $19,700 or equal payments at the end of each month for 8 years. What is the size of the monthly payments at 10. 43 compounded monthly? The payment is $___ (Round the final answer to the nearest cent as needed. Round all intermedlate valges to six docimal places as needed)

Answer 1

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.