Question $1$: SHOW WORK DO NOT USE EXCEL: Consider a coupon bond with an $8\%$ annual coupon rate, a $10\%$ interest rate, and a $$1000$ face value. The bond will mature in $4$ years. What is the duration of this bond? Duration is defined as a weighted average of the maturities of the cash payments. Suppose the weight assigned to the maturity of $1$ year is W$.$ Show how you determine W$.$ Round your intermediate steps and your final answers to $0\mathrm{.}0000.($e$.$g$.,$ round $0\mathrm{.}45674$ to $0\mathrm{.}4567)$

Show your work. No work, no credit. Hint: This question is similar to Example $1$ in "Examples for Homework $2."$