HW6 solution

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RMU *

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6005

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Finance

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Jan 9, 2024

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docx

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2

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Homework 6 1. If you deposit $2,000 in a bank account that pays 6% interest annually, how much will be in your account after 5 years? Formula: FV=PV*(1+i)n=2000*(1+0.06)5=2676.45 Calculator: N=5, I=6, PV=2000, PMT=0, solve for FV Excel: =FV(rate,nper,pmt,pv)=FV(0.06,5,0,2000) 2. What is the present value of a security that will pay $29,000 in 20 years if securities of equal risk pay 5% annually? Formula: PV=PV/(1+i)n=29,000/(1+0.05)20=10929.8 Calculator: N=20, I=5, FV=29000, PMT=0, solve for PV Excel: =PV(rate,nper,pmt,fv)=PV(0.05,20,0,29000) 3. Your parents will retire in 19 years. They currently have $350,000 saved, and they think they will need $800,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Calculator: N=19, PV=-350000, PMT=0, FV=800000, solve for I=4.45% Excel: =RATE(nper,pmt,pv,fv)=RATE(19,0,-350000,800000) 4. You have $33,556.25 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $220,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal? Calculator: I=12, PV=-33556.25, PMT=5000, FV=220000, solve for N=11 years Excel: =NPER(rate,pmt,pv,fv)=NPER(0.12,5000,-33556.25,220000) 5. Dick and Jane have a goal of accumulating $5,000,000 by the time they retire in 40 years. They plan to set aside an equal amount of money at the end of each of the next 40 years. Their investment account is expected to pay 5% compounded annually. How much money must they set aside each year to reach their goal? Calculator: N=40, I=5, PV=0, FV=5000000, solve for PMT=41,391 Excel: =PMT(rate,nper,pv,fv)=PMT(0.05,40,0,5000000) 6. Which of the following statements is true?
One dollar received now is always more valuable than a dollar received in the future In an annuity due the payments occur at the end of each time period Increasing the interest rate will increase the present value of a future cash flow Increasing the frequency of compounding will reduce the future value of a cash flow 7. Find the present value of an ordinary annuity which pays $300 per year for 6 years at 4%. Calculator: N=6, I=4, PMT=300, FV=0, solve for PV=1572.64 Excel: =PV(rate,nper,pmt,fv)=PV(0.04,6,300,0) 8. What is the present value of a $600 perpetuity if the interest rate is 5%? PV=PMT/i=600/5%=12,000 9. Find the present values of the following cash flow stream at a 5% discount rate: 0 1 2 3 4 5 CF, $ 0 150 450 450 450 250 PV=CF 1 /(1+i) 1 + CF 2 /(1+i) 2 + CF 3 /(1+i) 3 + CF 4 /(1+i) 4 + CF 5 /(1+i) 5 =150/(1+5%) 1 + 450/(1+5%) 2 + 450/(1+5%) 3 + 450/(1+5%) 4 + 250/(1+5) 5 =1,505.84 10. Your client is 26 years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $8,000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 10% in the future. How much will she have at 70? Calculator: N=44, I=10, PMT=8000, PV=0, solve for FV=5,221,126.09 Excel: =FV(rate,nper,pmt,pv)=FV(0.1,44,8000,0)
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