Equation question

CFA Level I Fixed Income
#1

The 4-year spot rate is 9.45%, and the 3-year spot rate is 9.85%. What is the 1-year forward rate three years from today?

Explanation
(1.0945)4 =(1.0985)3 × (1 + 3y1y)

3y1y = [(1.0945)^4 / (1.0985)^3] −1 = 8.258%

Approximate forward rate = 4(9.45%) − 3(9.85%) = 8.25%.

My Kaplan QuickSheet states the following:

Spot-Forward relationship:
(1+S2)^2 = (1+S1)(1+1y1y)

How can I use the QuickSheet formula on the problem above?

#2

If I want to invest money for 2 years, I have 2 ways to do this:

  1. Invest at the 2 year spot rate (left hand side of equation)
  2. Invest at the 1 year spot rate and reinvest at the 1 year forward rate 1 year from now (right hand side)

You can generalize this to n year spot and (n-1) year spot.