If the interest rates on one- to five-year bonds are currently 4%, 5%, 6%, 7% and 8%. The maturity premiums for one- to five-year bonds are 0%, 0.25%, 0.35%, 0.4% and 0.5%, respectively. Predict what the implied one-year interest rate will be two years from now?
A) 7.21%
B) 7.50%
C) 6.54%
D) 8.38%
E) 7.87%

Question

Quizplus · Accepted Answer

The implied one-year interest rate two years from now can be calculated using the forward rate formula, which involves the interest rates of bonds with different maturities. Given the interest rates and maturity premiums for one- to five-year bonds, we first need to find the actual interest rates by adding the maturity premiums to the given interest rates. The actual interest rates are: 1-year: 4%, 2-year: 5.25%, 3-year: 6.35%, 4-year: 7.4%, and 5-year: 8.5%. To find the implied one-year interest rate two years from now, we use the 3-year and 2-year rates. The formula for the forward rate is [(1+longer-term rate)^longer term / (1+shorter-term rate)^shorter term]^(1/(longer term - shorter term)) - 1. Applying this formula, we get [(1+6.35%)^3 / (1+5.25%)^2]^(1/(3-2)) - 1 = 7.50%.

If the Interest Rates on One- to Five-Year Bonds Are