options for first blank: 6.09% 7.00% 8.26% 9.45% options for second blank: 27.85
ID: 1171268 • Letter: O
Question
options for first blank: 6.09% 7.00% 8.26% 9.45%
options for second blank: 27.85 years 37.60 years 34.81 years 23.67 years
8. Implied interest rate and period Aa Aa Consider the case of the following annuities, and the need to compute either their expected rate of return or duration Tyler needed money for some unexpected expenses, so he borrowed $7,464.12 from a friend and agreed to repay the loan in eight equal installments of $1,250 at the end of each year. The agreement is offering an implied interest rate of Tyler's friend, Alfred, has hired a financial planner for advice on retirement. Considering Alfred's current expenses and expected future lifestyle changes, the financial planner has stated that once Alfred crosses a threshold of $5,581,702 in savings, he will have enough money for retirement. Alfred has nothing saved for his retirement yet, so he plans to start depositing $70,000 in a retirement fund at a fixed rate of 7.00% at the end of each year. It will take years for Alfred to reach his retirement goal.Explanation / Answer
1.Let the rate be x%
At this rate;present value of installments=$7464.12
7464.12=1250/1.0x+1250/1.0x^2+...........+1250/1.0x^8
Hence x=rate of interest=7%
2.
Future value of annuity=Annuity[(1+rate)^time period-1]/rate
5581702=70000[(1.07)^n-1]/0.07[where n=time period]
5581702=1,000,000[(1.07)^n-1]
[(1.07)^n-1]=(5581702/1,000,000)
(1.07)^n=(5581702/1,000,000)+1
=6.581702
Taking log on both sides;
n*log 1.07=log6.581702
Hence n=log6.581702/log 1.07
which is equal to
=27.85 years(Approx).
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