Assume a bank loan requires a interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight-year life.
a) How much could this loan be sold for to another bank if loans of similar quality carried a 8.5 percent interest rate?
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To determine how much this loan could be sold for to another bank, we need to calculate the present value of the loan's future cash flows.
The cash flows for this loan consist of the annual interest payment of $85 for eight years, as well as the final principal payment of $1,000.
To calculate the present value, we need to discount each of these cash flows using the 8.5 percent interest rate.
First, let's calculate the present value of the interest payments:
PV of interest payments = $85 / (1 + 0.085)^1 + $85 / (1 + 0.085)^2 + ... + $85 / (1 + 0.085)^8
Using the formula for the present value of an annuity, we can simplify this calculation:
PV of interest payments = $85 * [(1 - (1 / (1 + 0.085)^8)) / 0.085]
Next, let's calculate the present value of the principal payment:
PV of principal payment = $1,000 / (1 + 0.085)^8
Finally, we can calculate the present value of the entire loan:
PV of loan = PV of interest payments + PV of principal payment
Now, substitute the values into the formulas to get the answer.