You are exactly 28 years old and plan on contributing

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9. You are exactly 28 years old and plan on contributing (at the end of the month) $1000/month (and continuing each month until the age of 65) into your 401k retirement account. You expect to earn a 9% APR (with monthly compounding) in the account. How much would you expect to have in the retirement account exactly 37 years later, at age 65? 10. You are quoted two loan rates: 1) a 9% APR with weekly compounding and 2) a 9.2% APR with yearly compounding. Which one is truly the better offer? Do the necessary calculations to support your answer? 11. You are going to start a retirement saving plan. You are exactly 25 years old. You expect to retire in exactly 40 years. You expect to earn an APR of 5% (assuming monthly compounding). You want to have $2M in the account at retirement (in exactly 40 years). If you make (beginning of the month) monthly contributions into the account, how much does each payment have to be in order to reach the desired amount?
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Formula Sheet for Time-Value Problems Lump-sum: 𝑭𝑽 = 𝑷𝑽 ( 𝟏 + 𝒊 ) 𝒏 Ordinary annuities: 𝑷𝑽 𝒐𝒇 𝒐𝒓𝒅𝒊𝒏𝒂𝒓𝒚 𝒂𝒏𝒏𝒖𝒊𝒕𝒚 = 𝑪 𝒊 �𝟏 − 𝟏 ( 𝟏 + 𝒊 ) 𝒏 𝑭𝑽 𝒐𝒇 𝒐𝒓𝒅𝒊𝒏𝒂𝒓𝒚 𝒂𝒏𝒏𝒖𝒊𝒕𝒚 = 𝑪 𝒊 {( 𝟏 + 𝒊 ) 𝒏 − 𝟏 } Annuities due: 𝑷𝑽 𝒂𝒏𝒏𝒖𝒊𝒕𝒚 𝒅𝒖𝒆 = ( 𝟏 + 𝒊 ) 𝑷𝑽 𝒐𝒓𝒅𝒊𝒏𝒂𝒓𝒚 𝒂𝒏𝒏𝒖𝒊𝒕𝒚 = ( 𝟏 + 𝒊 ) 𝑪 𝒊 �𝟏 − 𝟏 ( 𝟏 + 𝒊 ) 𝒏 𝑭𝑽 𝒂𝒏𝒏𝒖𝒊𝒕𝒚 𝒅𝒖𝒆 = ( 𝟏 + 𝒊 ) 𝑭𝑽 𝒐𝒓𝒅𝒊𝒏𝒂𝒓𝒚 𝒂𝒏𝒏𝒖𝒊𝒕𝒚 = ( 𝟏 + 𝒊 ) 𝑪 𝒊 {( 𝟏 + 𝒊 ) 𝒏 − 𝟏 } Logarithms: 𝐥𝐧 𝒂 𝒏 = 𝒏 𝐥𝐧 𝒂 Effective Rate: 𝑬𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆 𝒂𝒏𝒏𝒖𝒂𝒍 𝒓𝒂𝒕𝒆 ( 𝑬𝑨𝑹 ) = �𝟏 + 𝑨𝑷𝑹 𝒎 𝒎 − 𝟏 m = # of compounding periods per year APR = annual “quoted” rate
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