##### Question

# Your Retirement part II The 30-year United States Treasury bond is currently yielding about 287%. After reviewing Quiz 4, you decide you want to have $1,000,000 worth of bonds to begin your retir…

Your Retirement part II The 30-year United States Treasury bond is currently yielding about 287%. After reviewing Quiz 4, you decide you want to have $1,000,000 worth of bonds to begin your retirement, because the interest earned from a bank's savings account is lousy. Assuming you make annual purchases of 30-year Treasury bonds (think 2.87% annual interest), how much do you need to purchase each year in order to have $1,000,000 at the end of 35 years? Hint: Suppose y(t) reports the value of your bondst years from now. Let X – how much you plan to buy each year, then solve the differential equion 0329 yitj+xy(0) 0, leaving X in your answer temporarily. Lastly solve y(35) – 1,000,000 for X. 6)

Your Retirement part II The 30-year United States Treasury bond is currently yielding about 287%. After reviewing Quiz 4, you decide you want to have $1,000,000 worth of bonds to begin your retirement, because the interest earned from a bank's savings account is lousy. Assuming you make annual purchases of 30-year Treasury bonds (think 2.87% annual interest), how much do you need to purchase each year in order to have $1,000,000 at the end of 35 years? Hint: Suppose y(t) reports the value of your bondst years from now. Let X – how much you plan to buy each year, then solve the differential equion 0329 yitj+xy(0) 0, leaving X in your answer temporarily. Lastly solve y(35) – 1,000,000 for X. 6)

## Solutions

##### Expert Solution

Soiution Given thot The 3ote of 9nte est 0.87 tet x amount op Plant punchoses besch ye chases bond t- yeoshs from nou, The diffeenta io: ioo yo) – o and beiring is The volnebond whOR , χ ·IS Constant dlt cl Tntegvctinj both side s dl e tt C rat cnstant

At to hen, he equations kn 0987 The er of 35 eons, o 62S7 28,700 → It =e. eveay ym, Puschase needs to be 4|16, 53 у.YI8

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