9. On January 1, 2008, Adele invested $150,000. The following table shows her av
ID: 2809823 • Letter: 9
Question
9. On January 1, 2008, Adele invested $150,000. The following table shows her average annual rates of return for periods ending on January 1, 2018: 1-year 2-year 5-year 10-year 3.5% | 1% 5% 7% (a) Find the balance of Adele's portfolio on January 1, 2018. (b) Find the balance of Adele's portfolio on January 1, 2013. (c) Find Adele's average annual rate of return for the 3-year period from January 1, 2013 (d) Suppose that the annual rate of inflation in 2017 was 1.9%. Find the inflation-adjusted [Hint: 150000 (1.05)5 $191, 442.23 is not the correct answer.] until January 1, 2016 average rate of return of Adele's portfolio for the 1-year period from January 1, 2017 to January 1, 2018. [Hint: Real interest rate.]Explanation / Answer
From the table, we construct the below :
2008-2018:7%
2013-2018:5%
2016-2018:1%
2017-2018:3.5%
1.
Rate for 2008-2018=7%
So, balance at 2018=150000*(1+rate for 2008-2018)^10=150000*1.07^10=295072.7036
2.
(1+rate for 2008-2013)^5*(1+rate for 2013-2018)^5=(1+rate for 2008-2018)^10
=>(1+rate for 2008-2013)^5=((1+rate for 2008-2018)^10)/((1+rate for 2013-2018)^5)
So, balance at 2013=150000*(1+rate for 2008-2013)^5=150000*(1.07^10)/(1.05^5)=231197.1843
3.
(1+rate for 2013-2016)^3*(1+rate for 2016-2018)^2=(1+rate for 2013-2018)^5
=>rate for 2003-2016=((1.05^5)/(1.01^2))^(1/3)-1=7.7543%
4.
(1+real rate)*(1+inflation)=(1+nominal rate)
=>real rate=(1+3.5%)/(1+1.9%)-1=1.5702%
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