.impiea interest rate, perioa, and payments Aa Aa Present value of annuities is
ID: 2808773 • Letter: #
Question
.impiea interest rate, perioa, and payments Aa Aa Present value of annuities is also used to calculate the rate of return expected from an investment and, thus, has several practical applications Aakash inherited an annuity worth $5,727.01 from his uncle. The annuity will pay him seven equal payments of $1,100 at the end of each year. What rate of return is the annuity fund offering? 10.80% 6.96% 9.44% 8.00% Aakash's friend Rafael has hired a financial planner for advice on retirement. Considering Rafael's current expenses and expected future lifestyle changes, the financial planner has stated that once Rafael crosses a threshold of $5,817,486 in savings, he will have enough money for retirement. Rafael has nothing saved for his retirement yet, so he plans to start depositing $55,000 in a retirement fund at a fixed rate of 8.00% at the end of each year. How long will it take for Rafael to reach his retirement goal? O 36.50 years O 24.82 years O 29.20 years O 39.42 yearsExplanation / Answer
a.Let rate of return be x%
At this rate;present value of annuity=5727.01
5727.01=1100/1.0x+1100/1.0x^2+..............+1100/1.0x^7
Hence x=rate of return=8%
2.
Future value of annuity=Annuity[(1+rate)^time period-1]/rate
5,817,486=55000[(1.08)^n-1]/0.08
5,817,486=687500[(1.08)^n-1]
5,817,486/687500=[(1.08)^n-1]
[(1.08)^n-1]=8.461797818
(1.08)^n=9.461797818
Taking log on both sides;
n*log(1.08)=log9.461797818
n=log9.461797818/log(1.08)
=29.20 years(Approx).
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