he rate interpreted to be the incremental return for extending the time-to-maturity of an investment for an additional time period is the:

The rate interpreted to be the incremental return for extending the time-to-maturity of an investment for an additional time period is known as the Forward Rate.

Here's a step-by-step explanation:

1. When you invest in a financial instrument, you expect a certain return on your investment. This return is often expressed as an interest rate.

2. The time-to-maturity of an investment is the time period for which the investment is held before it is returned to the investor.

3. If you decide to extend the time-to-maturity of your investment for an additional time period, you would expect an additional return for the extra time your money is invested.

4. This additional return is what is referred to as the Forward Rate. It is the rate that you would receive if you decided to invest your money for an additional time period, given the current interest rates.

5. The Forward Rate is a concept used in finance to compare the returns of different investments with different maturities. It helps investors make decisions about where to invest their money for the best possible return.