Two debts ---- the first of $800 due six months ago and the second of $1400 borrowed one year ago for a term of three years at 6.5% compounded annually ---- are to be replaced by a single payment one year from now. Determine the size of the replacement payment if interest is 7.5% compounded quarterly and the focal date is one year from now.
To determine the size of the replacement payment, we need to calculate the future value of the two debts using the given interest rates and compounding periods.
Let's start with the first debt of $800, which was due six months ago. To find the future value, we need to bring it to the focal date (one year from now) with the interest rate of 7.5% compounded quarterly.
First, let's find the number of compounding periods between the due date and the focal date:
Number of periods = (1 year - 6 months) * (4 quarters / 1 year) = 2 quarters
Next, we can calculate the future value of the first debt:
Future Value (first debt) = $800 * (1 + (7.5% / 4))^2
Now, let's focus on the second debt of $1400 borrowed one year ago for a term of three years at 6.5% compounded annually. Since it has already been one year, we need to calculate the future value for two more years.
Future Value (second debt) = $1400 * (1 + (6.5% / 1))^2
Now, we add the future values of both debts to get the total replacement payment one year from now:
Replacement payment = Future Value (first debt) + Future Value (second debt)
By plugging in the values and calculating, you can find the size of the replacement payment.