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# Annuities, Perpetuity, Savings Account, Bonds

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30. Your brother has offered to give you \$100, starting next year, and after that growing at 3% for the next 20 years. You would like to calculate the value of this offer by calculating how much money you would need to deposit in the local bank so that the account will generate the same cash flows as he is offering you. Your local bank will guarantee a 6% annual interest rate so long as you have money in the account.

a. How much money will you need to deposit into the account today?
b. Using an Excel spreadsheet, show explicitly that you can deposit this amount of money into the account, and every year withdraw what your brother has promised, leaving the account with nothing after the last withdrawal.

31. You have decided to buy perpetuity. The bond makes one payment at the end of every year forever and has an interest rate of 5%. If you initially put \$1000 into the bond, what is the payment every year?

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Question 30A Question 31
Annuity \$100 Interest rate 5%
Annuity growth 3% Investment \$1,000