Two payments of $2,000 each are scheduled for six months from now and two years from now. They are to be re-scheduled as follows: a payment one year from now and a second payment, half the size of the first payment, three years from now. What must the amount of each payment be for the replacement stream to be equivalent to the originally scheduled stream? Assume that money can earn 7.8% compounded semi-annually.

Compounded Semi-Annually

This is the process where interest is added to the principal sum of a loan or deposit twice a year, resulting in interest being earned on interest from that point on.

Replacement Stream

A series of cash flows intended to replace the benefits of an asset or investment over time.

Payments

Payments refer to the amounts of money transferred from one party to another as compensation for goods or services, or as fulfillment of an obligation.