EDIT: THIS WAS THE EXAMPLE WITHOUT YEARS CAN YOU EXPLAN THE METHODS WITHOUT EXCE
ID: 3144975 • Letter: E
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EDIT: THIS WAS THE EXAMPLE WITHOUT YEARS CAN YOU EXPLAN THE METHODS WITHOUT EXCEL?
An endowment is set up to provide scholarships in perpetuity. Each scholarship is awarded at the end of each year. The first 8 scholarships are for $2,000. After that, the scholarships will be awarded in the amount of $500. The account earns an annual effective rate of 5%. Determine the present value of the endowment.
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An endowment is set up to provide scholarships in perpetuity. Each scholarship is awarded at the end of each year. The first 9 scholarships are for $1,800. After that, the scholarships will be awarded in the amount of $750. The account earns an annual effective rate of 6.1%. Determine the present value of the endowment Expert Answer Anonvmous answered this 5,917 answers Was this answer helpful? B11 f, =1800+750/6.1% Year! Cash flow | PVF @6.10% | Present value 1.000 $ 0.943$ 1,696.51 0.888 $ 1,598.98 0.837 $ 1,507.05 0.789 $ 1,420.40 0.744 $ 1,338.74 0.701 $ 1,261.77 0.661 $ 1,189.23 0.623 1,120.86 0.587$ 8,272.35 0 3 1 1,800.00 4 2 1,800.00 5 3$ 1,800.00 6 4 1,800.00 7 5 1,800.00 8 6 $ 1,800.00 9 7$ 1,800.00 10 8 S 1,800.00 11 9 $14,095.08 12 13 Present value of endowment19,405.88Explanation / Answer
Present value for first 8 years is
PV = PMT ( 1 - (1+i)-n /i)
Where PMT is yearly payment , i is annual rate of interest and n is number of years.
= 2000 ( 1 - (1.05)-8 / 0.05)
Present value after 8 years is perpetuity,
PV = (1+i)-n PMT / i
Where we multiply PMT/i by discount factor (1+i)-n
PV = 1.05-8 * 500 / 0.05
Therefore,
PV for endowment = PV for first 8 years + pv after 8 years
= 2000 ( 1 - (1.05)-8 / 0.05) + 1.05-8 * 500 / 0.05
= 12926.42 + 6768.40
= 19694.82
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