A $$5000$ loan at $10\%$ compounded annually is to be repaid by two payments three and five years from the date of the loan. The first payment of $$3000$ will be applied to the balance owed after conversion of interest to principal at the end of the first three years. What would an investor pay for the loan contract $20$ months after the date of the loan if she requires a rate of return of $9\%$ compounded monthly?