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Bookmarks People WindowHelp Aplia: Student Question ? MindTap-Cengage Learning x os://courses.aplia.com/af/servlet/quiz?quiz action takeQuiz&q; uiz probGuid-ONAPCOA8010100000041ca25e01000008 er II 2018 Aaron Plantt Home Grades Personalized Reviews Discussion Course Materials Time Value of Money Graded Assignment | Read Chapter 5 | Back to Assignment Due Sunday 06.17.18 at 11:45 PM Keep the Highest: 12 Attempts: 13. Implied interest rate and period Consider the case of the following annuities, and the need to compute either their expected rate of return or duration. Anthony inherited an annuity worth $3,742.22 from his undle. The annuity will pay him three equal payments of $1,400 at the end of each year. The annuity fund is offering a return of Anthony's friend, Sachit, has hired a financial planner for advice on retirement. Considering Sachit's current expenses and expected future lifestyle changes, the financial planner has stated that once Sachit crosses a threshold of $8,416,371 in savings, he will have enough money for retirement. Sachit has nothing saved for his retirement yet, so he plans to start depositing $85,000 in a retirement fund at a fixed rate of 6.00% at the end of each year. It will take years for Sachit to reach his retirement goal. Continue without saving 17

Explanation / Answer

Amount received from the annuity fund=$1,400 each year for 3 years.

So total amount received=1,400*3=$4,200

Inherited amount=$3,742.22

Return=(4,200-3,742.22)/3742.22=0.1223 or 12.23%

Savings needed= $8,416,371

Annual deposit=$85,000

Rate=6% or 0.06

Thus, according to compound interest formula,

Amount=Principal(1+rate)years

(1+rate)years=Amount/Principal

Putting the given values, we have:

(1+0.06)years=8,416,371/85,000

1.06years=99.02

Taking log on both sides,

years*log 1.06=Log 99.02

years*0.0253=1.9957

years=78.88 that is 79 years

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