Forward and spot rates

Suppose the 3-year spot rate is 12.1% and the 2-year spot rate is 11.3%. Which of the following statements concerning forward and spot rates is most accurate? The 1-year:
A) forward rate one year from today is 13.7%.
B) forward rate two years from today is 13.2%.
C) forward rate two years from today is 13.7%.

The answer is C.

I don’t understand the concept of this topic. Can somebody please explain the concept and then this question please. What is it all about? Thanks in advance.

For spot and forward rates, an investor has a choice: invest at the n-year spot rate OR invest at a shorter spot rate and reinvest at an implied forward rate up to time n. To avoid arbitrage, the two strategies must produce the same future value.

In the above example, the question is testing whether you understand when the implied future rate starts and how long it runs. You have a choice between investing for 3 years OR for 2 years and then reinvest for 1 more year. Under the reinvestment strategy, I invest for 2 years, so we can eliminate A. Since B and C use the same starting point of time 2 and a 1 year investment period, we have to do some algebra:

1.121^3 = 1.113^2 * (1 + forward rate)
1.121^3 / 1.113^2 = 1 + forward rate
1.1371729 = 1 + forward rate
forward rate = 0.1371729