(PLEASE SHOW ALL WORK AND VALUES) (PLEASE SHOW ALL WORK AND VALUES) 35) Fill in
ID: 2811990 • Letter: #
Question
(PLEASE SHOW ALL WORK AND VALUES)
(PLEASE SHOW ALL WORK AND VALUES)
35) Fill in the missing annual interest rates in the following table for an ordinary annuity stream. Number of Annual Future ValueAnnuity Present Value Payments or YearsInterest Rate 10 20 30 100 $500.00 $346.97 $1,946.7:3 S1,044,010.06$400.00 0 $25,000.00 0 S3,680.04 0 $20,000.00 0 36) What are you getting in terms of interest rate if you are willing to pay S15,000 today for an annual stream of payments of S2,000 for the next twenty years? The next forty years? The next one hundred years? Forever? 37) A local government is about to run a lottery, but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust to pay the lump-sum payout to the trust and have the trust (probably a local bank) pay the annual payments. The first winner of the lottery chooses the annuity and will receive S150,000a year for the next twenty-five years. The local government will give the trust $2,000,000 to pay for this annuity. What investment rate must the trust earn to break even on this arrangement?Explanation / Answer
Present Value=Annuity/Interest Rate*(1-1/(1+interest rate)^number of years)
Future Value=Annuity/Interest Rate*((1+interest rate)^number of years-1)
1.
2.
15000=2000/r*(1-1/(1+r)^20)
=>r=11.9349564494087%
15000=2000/r*(1-1/(1+r)^40)
=>r=13.2411246200319%
15000=2000/r*(1-1/(1+r)^100)
=>r=13.3332836071022%
15000=2000/r
=>r=13.3333333333333%
3.
2000000=150000/r*(1-1/(1+r)^25)
=>r=5.56185776175064%
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