Using Excel calculate the future value of $$100$ for $1-30$ years. Assume the interest rate is $3\%.$

Find the exact number of years it takes for an investment to double if interest rates are $1\%,2\%,3\%,4\%,5\%.$ How does this compare to the rule of $70.$

Using Excel calculate the Internal Rate of Return of an investment that costs $$2,000,000$ in year $1($with no other operating costs$)$ and pays $$250,000$ for the next $15$ years starting in year $2.$

Using Excel calculate the fixed annual payment of a $$500,000$ loan for $20$ years with an annual interest rate of $4\%.$

Suppose you plan on retiring when you$$re $50$ years old. You anticipate spending $$100,000$ per year and living until you are $90.$ If you assume interest rates are $4\%,$ how much will you need to to retire? Find the amount of saving you need when you$$re $50$ years old.

On $1/1/2021$ you purchase a $3-$year coupon bond that matures on $12/31/2023.$ The coupon rate is $4\%$ and the coupon payment occurs at the end of each year. The bond has a face value of $$1000.$

If the yield to maturity equals the coupon rate what is the price of the bond, explain. Write down the equation you would use to calculate the price of the bond with interest rate i$.$

In the beginning of $2022$ you are considering selling the bond. The bond has $2$ years until maturity. The buyer will receive a coupon payment at the end of $2022$ and $2023$ plus the face value at maturity. The interest rate during $2022$ and $2023$ is expected to be $6\%.$ At what price do you sell the bond?

Assuming you sell the bond what is your rate of return on this bond? Assume you initially purchased the bond for $$1000.$

Why is the rate of return different than the yield to maturity.

Under what conditions will a discount bond have a negative nominal interest rate? Is it possible for a coupon bond or a perpetuity to have a negative nominal interest rate?

If interest rates decline, which would you rather be holding, long$-$term bonds or short$-$term bonds? Why? Which type of bond has the greater interest$-$rate risk?